SSC CGL 2025 (Held On: 14 Sept, 2025 Shift 2) (Previous Year Paper)

The logic followed here is:

So, 'KLV' will replace the question mark in the given series.

Hence, the correct answer is "Option 2".

The logic followed here is:

So, 'RIB' will replace the question mark in the given series.

Hence, the correct answer is "Option 4".

BODMAS Table: 

Given:

'÷' means '+'

'-' means '×'

'+' means '-'

'×' means '÷'

Given equation:

42 × 28 - 30 ÷ 48 + 45 = ?

Now replace the signs accordingly:

⇒ 42 ÷ 28 × 30 + 48 - 45

Now solve step by step:

⇒ 42 ÷ 28 = 1.5

⇒ 1.5 × 30 = 45

⇒ 45 + 48 - 45

⇒ 93 - 45

⇒ 48

Hence, the correct answer is "Option 4".

The logic followed here is:

thus, "98" will replace the question mark in the given series.

Hence, the correct option is "Option 2".

Given:

Statement:

The rapid advancement of automation and artificial intelligence could lead to significant job displacement, but it also presents an opportunity to create new jobs in emerging industries.

Assumptions:

I. Automation and AI could cause job losses in some sectors – True (The statement clearly mentions “job displacement,” which assumes that automation and AI may cause job losses).

II. New industries will emerge as a result of automation and AI – True (The statement says there is an opportunity to create new jobs in emerging industries, which assumes new industries will develop).

III. The displacement caused by automation is temporary and will be reversed by new industries – False (The statement does not assume that job losses will be completely reversed or that the displacement is temporary; it only mentions an opportunity for new jobs).

So, Only assumptions I and II are implicit.

Hence, the correct answer is "Option 1".

Given word: FRIEND

Arrange letters in alphabetical order: D, E, F, I, N, R

Compare positions:

Position 1: F ≠ D

Position 2: R ≠ E

Position 3: I ≠ F

Position 4: E ≠ I

Position 5: N = N

Position 6: D ≠ R

So, Only N (position 5) remains unchanged → 1 letter

Hence, the correct answer is "Option 1".

The address given in the problem is:

Shruti Bansal E-55, Palm Greens, Faridabad, 121002

Now, match this address with the given options:

So, address Option 2 is exactly identical to the given address.

Hence, the correct answer is Option 2.

Given word: UNIVERSAL

Arrange letters in alphabetical order: A, E, I, L, N, R, S, U, V

New letter cluster: A E I L N R S U V

Second from the left = E

Fifth from the right:

Counting from right → V (1), U (2), S (3), R (4), N (5)

So the fifth from the right = N

Now ,

Alphabet positions:

E = 5

N = 14

Thus,Letters between them = 14 − 5 − 1 = 8

Hence, the correct answer is "Option 2".

Given options:

Option 1) Photoshop

​⇒ It is a raster graphics editing software mainly used for photo editing, image manipulation, and digital art.

Option 2) Illustrator

​⇒ It is a vector graphics design software used for creating logos, icons, illustrations, and scalable artwork.

Option 3) CorelDRAW

​⇒ It is also a vector graphics editor used for designing logos, layouts, banners, and other graphic materials.

Option 4) Linux

⇒ It is an operating system used to run computers and software applications. It is not a graphic designing software.

Linux is an operating system, not a graphic designing software.

Hence, the correct answer is "Option 4".

The logic followed here is:

Logic: Each letter of the word is shifted 3 steps backward in the English alphabetical order.

For, DEVIL → ABSFI

Similarly, For OTHER:

So, OTHER becomes LQEBO.

Hence, the correct answer is "Option 3".

The logic followed here is:

Logic: Each letter is shifted 2 steps forward in the English alphabetical order.

For, MASTER → OCUVGT

Similarly, For LABOUR:

So, LABOUR becomes NCDQWT.

Hence, the correct answer is "Option 1".

The logic followed here is:

Series:  11, 13, 17, 19, ?

All the numbers are prime numbers.

Prime numbers in order:

11, 13, 17, 19, 23 …

thus, "23" will replace the question mark in the given series.

Hence, the correct option is "Option 2".

The logic followed here is:

Now, checking the given options:

Option 1: A1@ : C3# : E5$

Letters → A, C, E (each +2)

Numbers → 1, 3, 5 (each +2)

Option 2: B2% : D4^ : F6&

Letters → B, D, F (each +2)

Numbers → 2, 4, 6 (each +2)

Option 3: C3* : E5( : G7)

Letters → C, E, G (each +2)

Numbers → 3, 5, 7 (each +2)

Option 4: D4_ : F6@ : I9&

Letters → D, F, I

D → F (+2)

F → I (+3) (pattern breaks)

and Numbers → 4, 6, 9

4 → 6 (+2)

6 → 9 (+3) (pattern breaks)

Thus, D4_ : F6@ : I9& does not follow the same +2 pattern in letters and numbers.

Hence, the correct answer is "Option 4".

Given:

Total balls = 5 red + 3 blue + 2 green = 10 balls

Now, Non-green balls = Red + Blue

= 5 + 3

= 8

So, Probability of drawing a non-green ball =

= 8 / 10

= 0.8

Hence, the correct answer is "Option 2".

The logic followed here is:

​Logic: a @ b = (a + b) × b

Given:

9 @ 3 = 36

→ (9 + 3) × 3

= 12 × 3

= 36

6 @ 2 = 16

→ (6 + 2) × 2

= 8 × 2

= 16

Now, For 8 @ 2 :

8 @ 2 = (8 + 2) × 2

= 10 × 2

= 20

Hence, the correct answer is "Option 1".

The logic followed here is:

Given:

"The music sounds sweet" → la ma na ta

"The music sounds loud" → la ma pa ta

"The song sounds sweet" → ka ma na ta

So, the code is: ka ma ta pa

Hence, the correct answer is "Option 4".

The logic followed here is:

'ABCDE' is coded as 'EDCBA'

ABCDE → Reverse order → EDCBA

'FGHIJ' is coded as 'JIHGF'

FGHIJ → Reverse order → JIHGF

And,

'KLMNO' is coded as 'ONMLK'

KLMNO → Reverse order → ONMLK

Similarly,

'PQRST' is coded as

PQRST → Reverse order → TSRQP 

Hence, the correct answer is "Option 1".

The logic followed here is:

Logic: a $ b = (a − b) × b

Given:

9 $ 3 = 18

→ (9 − 3) × 3

= 6 × 3

= 18

8 $ 2 = 12

→ (8 − 2) × 2

= 6 × 2

= 12

Now, For 6 $ 4 :

6 $ 4 = (6 − 4) × 4

= 2 × 4

= 8

Hence, the correct answer is "Option 1".

Given:

Total solution = 25 L

Sugar : Water = 3 : 2

Total parts = 3 + 2 = 5

Sugar = (3/5) × 25 = 15 L

Water = (2/5) × 25 = 10 L

Now, Sugar : Water = 1 : 1

Sugar is already 15 L, so water must also be 15 L.

Currently water = 10 L

So, Water to be added = 15 − 10 = 5 L

Hence, the correct answer is "Option 2".

Family Chart:

Given: 

1.Ravi is married to Rekha.

2.Rekha's brother is Ramesh.

3.Ramesh's wife is Rina.

4.Rina's son is Raj.

So, Raj is Ravi’s Nephew.

Hence, the correct answer is "Option 1".

Family Chart:

Given: 

1. My mother's father = My maternal grandfather.

2. The only daughter of my maternal grandfather = My mother (since she is his only daughter).

So, the man is Seema’s Brother.

Hence, the correct answer is "Option 3".

BODMAS Table: 

Given condition: Interchange ‘+’ and ‘×’ and 15 & 30

Now, check each option after interchanging:

Option 1) (15 + 2) × 30 = 60

After interchange:

(30 × 2) + 15 = ?

⇒ 60 + 15 = 75 ≠ 60 (False)

Option 2) (30 + 3) × 15 = 40

After interchange:

(15 × 3) + 30 = ?

⇒ 45 + 30 = 75 ≠ 40 (False)

Option 3) (15 + 4) × 30 = 135

After interchange:

(30 × 4) + 15 = ?

⇒ 120 + 15 = 135 = 135 (True)

Option 4) (30 + 1) × 15 = 40

After interchange:

(15 × 1) + 30 = ?

⇒ 15 + 30 = 45 ≠ 40 (False)

Hence, the correct answer is "Option 3".

Given Statement: M > N ≤ O

Now,

Conclusions:

(i) M > O → False (From M > N and N ≤ O, no definite relation between M and O)

(ii) M ≥ O → False (Again, no definite relation between M and O can be established)

Here, Neither conclusion I nor II is true.

Hence, the correct answer is "Option 4".

BODMAS Table: 

Given equation: 20 + 5 × 2 - 10 = ?

Now, if ‘+’ means ‘×’, ‘×’ means ‘-’, and ‘-’ means ‘÷’, then:

⇒ 20 × 5 - 2 ÷ 10 = ?

⇒ 100 - 2 ÷ 10 = ?

⇒ 100 - 0.2 = ?

⇒ 99.8

Hence, the correct answer is "Option 4".

According to the question:

Let, the unit place digit be: "x".

Let, the tens place digit be: "y".

Therefore, the number will be:

10y + x.

According to the question, this two-digit number is 4 times  the sum of digits.

→ 4(x + y) = 10y + x.

→ 4x + 4y = 10y + x.

→ 3x = 6y.

→ x = (2)y ----(1).

Now, the new number is 18 more than the original if the digits are reversed.

→ 10y + x = 10x + y + 18

→ 9y - 18 = 9x

Putting the value of "x" from the equation (1)

→ 9y - 18 = 9(2)y

→ 9y - 18 = 18y

→ 9y = 18

→ y = 2

Putting the value of "y" in equation (1).

→ x = (2) × 2

→ x = 4

As the tense digit is 2 and one digit is 4.

The number is "24".

Hence, the correct answer is "Option 1".

The correct answer is The last harvest representing survival and love.

Key Points

• The Mim Kut festival is a significant cultural event celebrated by the Mizo tribe in Northeast India, particularly in Mizoram.
• The term "Mim" refers to maize, which is the central crop associated with the festival and symbolizes the last harvest of the year.
• The festival highlights the themes of survival and love, as it is a time to express gratitude for the harvest and remember loved ones who have passed away.
• Traditional practices such as offering maize, bread, and other local delicacies to spirits and ancestors are central to the celebrations.
• The Mim Kut festival is also marked by vibrant cultural performances, traditional dances, and community feasts that showcase the unity and cultural heritage of the Mizo people.

Additional Information​

• Major Festivals by State
• Assam:
• Bihu: Three festivals (Rongali, Kati, Bhogali) marking seasons, New Year, and harvest with dancing, feasting, and bonfires.
• Ambubachi Mela: Major Hindu fair at Kamakhya Temple in June.
• Jonbeel Mela: A unique barter trade festival.
• Nagaland:
• Hornbill Festival: A 10-day-long celebration of Naga tribes' culture in December.
• Aoling Festival: Konyak tribe's spring festival.
• Moatsu Mong: Ao tribe's post-sowing festival.
• Arunachal Pradesh:
• Ziro Festival of Music: An acclaimed outdoor music festival.
• Losar: Tibetan Buddhist New Year in Tawang.
• Dree Festival: Apatani tribe's agricultural festival.
• Mopin: Galo tribe's harvest festival.
• Meghalaya:
• Wangala: Garo tribe's "100 Drums" harvest festival.
• Nongkrem Dance Festival: Khasi harvest festival.

The correct answer is 14.

Key Points

• The Kharchi Puja is an important festival celebrated in Tripura, India, dedicated to the worship of 14 deities.
• The word "Kharchi" is derived from two Tripuri words: "Khar" (sin) and "chi" (cleaning), symbolizing the purification of sins and the worship of the deities.
• The 14 deities represent the guardians of Tripura, each deity being associated with specific aspects of nature, culture, and governance.
• The festival is celebrated annually in the month of July in the temple of 14 gods located in Old Agartala.
• Kharchi Puja is marked by elaborate rituals, offerings, cultural performances, and prayers that emphasize the harmony between humans and nature.
• The deities are worshipped for their blessings and protection, and the festival is a major cultural and religious highlight of Tripura.

Additional Information

• Major Festivals
• Garia Puja: A vibrant tribal festival for health and harvest, honoring the bamboo deity Baba Garia, with rituals, music, and dance.
• Kharchi Puja: A significant religious festival at Puran Haveli, worshipping 14 deities for purification and well-being, known for its unique rituals and folk performances.
• Ker Puja: A secretive but crucial festival dedicated to the guardian deity of the royal family, ensuring the state's protection.
• Durga Puja & Diwali: Celebrated with great fervor, especially at the Tripura Sundari Temple (Matabari).

The correct answer is Both 1 and 2 are correct.

Key Points

• Mughal architecture is renowned for blending Persian, Islamic, Turkish, and Indian styles, resulting in a unique and harmonious Indo-Islamic architectural aesthetic.
• It emphasized symmetry, grandeur, and the use of geometrical designs, which were heavily influenced by Persian and Central Asian traditions.
• Red sandstone and white marble were the most commonly used materials, as seen in iconic structures like the Red Fort (sandstone) and the Taj Mahal (white marble).
• Some of the most famous Mughal architectural marvels include the Humayun’s Tomb, Taj Mahal, Jama Masjid, and Fatehpur Sikri, which showcase artistic finesse and innovation.
• Structures were often adorned with intricate carvings, floral motifs, calligraphy, and pietra dura (inlay work using precious and semi-precious stones).

Additional Information

• Mughal architecture:
• This synthesis of styles was a hallmark of the Mughal era, reflecting the rulers’ cultural inclusivity.
• The use of domes, minarets, arches, and gardens (Charbagh style) are prominent features derived from Persian and Islamic architecture.
• Indian architectural elements like chhatris (elevated dome-shaped pavilions) and jalis (intricate lattice screens) were also incorporated into Mughal structures.

The correct answer is A dribble ends when both hands touch the ball once..

Key Points

• In basketball, a dribble ends when a player uses both hands to touch the ball simultaneously or when the ball comes to rest in one or both hands.
• This rule is enforced to maintain the flow of the game and prevent unfair advantages that could arise from manipulating the ball with both hands.
• Once a dribble ends, the player cannot resume dribbling the ball; doing so constitutes a "double dribble" violation.
• After the dribble ends, the player must either pass the ball to a teammate or attempt a shot.
• The dribble is a fundamental basketball skill used to advance the ball, evade defenders, or create opportunities for passing and shooting.

Additional Information

• Fundamental Skills
• Dribbling: Bouncing the ball continuously with one hand while moving; essential for ball control and advancing.
• Passing: Moving the ball to teammates using chest, bounce, or overhead passes to create scoring chances.
• Shooting: Throwing the ball into the basket (layups, jump shots, free throws).
• Defense: Preventing the opponent from scoring through man-to-man, zone, or blocking shots.
• Rebounding: Gaining possession of missed shots.

The correct answer is Sheetal Devi and Rakesh Kumar.

Key Points

• Sheetal Devi and Rakesh Kumar won the bronze medal in the Mixed Team Compound Open Archery event during the Paris 2024 Paralympics.
• They showcased exceptional skills and teamwork, earning a podium finish for India in the prestigious global event.
• The Mixed Team Compound Open Archery event features teams composed of one male and one female archer, emphasizing coordination and precision.
• Sheetal Devi is recognized as one of India's promising para-archers, while Rakesh Kumar has been a consistent performer in international para-archery tournaments.
• Their achievement contributed to India's growing reputation in para-sports and inspired budding athletes across the nation.

Additional Information

• Harvinder Singh and Jyoti Baliyan
• Harvinder Singh is an accomplished para-archer who won a bronze medal at the Tokyo 2020 Paralympics in the men's individual recurve event.
• Jyoti Baliyan is one of India’s top para-archers who has represented the country in multiple international competitions.
• Although both are celebrated athletes, they did not win the bronze medal in the Mixed Team Compound Open Archery at the Paris 2024 Paralympics.
• Sheetal Devi and Harvinder Singh
• While both Sheetal Devi and Harvinder Singh are prominent para-archers, they did not team up for the Mixed Team Compound Open event at the Paris 2024 Paralympics.
• Harvinder Singh specializes in the recurve bow category, whereas Sheetal Devi competed in the compound bow category.
• Rakesh Kumar and Vivek Chikara
• Rakesh Kumar is a renowned para-archer specializing in compound archery and has consistently performed well in international tournaments.
• Vivek Chikara is another talented para-archer; however, they did not participate as a team in the Mixed Team Compound Open Archery event at Paris 2024.

The correct answer is São Paulo.

Key Points

• The Americas Regional Office of the New Development Bank (NDB) was announced to be established in São Paulo, Brazil, during the BRICS Foreign Ministers' Meeting in 2018.
• São Paulo, being one of the largest and most economically significant cities in Brazil, was selected to bolster the NDB's engagement in the Americas region.
• The New Development Bank, established by the BRICS nations (Brazil, Russia, India, China, and South Africa), aims to mobilize resources for infrastructure and sustainable development projects in emerging economies.
• The Americas Regional Office in São Paulo plays a crucial role in identifying and financing development projects in the region, particularly focusing on areas such as energy, transport, and urban development.
• The establishment of this office underscores the NDB's commitment to enhancing its global outreach and strengthening collaboration with member countries in the Americas.

Additional Information

• Mexico City:
• Mexico City is the capital and largest city of Mexico, known for being a cultural and financial hub in Latin America.
• While it is a prominent city in the Americas, it was not chosen for the establishment of the NDB's Americas Regional Office.
• Buenos Aires:
• Buenos Aires is the capital of Argentina and a major economic center in South America.
• It plays a significant role in regional trade and finance but was not selected as the location for the NDB's regional office.
• Lima:
• Lima is the capital of Peru and an important city in the Pacific region of South America.
• Despite its strategic position, it was not chosen as the location for the NDB's Americas Regional Office.
• New Development Bank (NDB):
• The NDB was established in 2014 by the BRICS nations to support infrastructure and sustainable development projects in emerging economies.
• The bank's headquarters is located in Shanghai, China, and it has regional offices in South Africa, Russia, and Brazil.
• The institution aims to foster economic growth, reduce the infrastructure gap, and promote sustainable development in member countries.

The correct answer is Language's role in social justice.

Key Points

• The book "Because Words Matter" highlights the significance of language as a tool for shaping social discourse and advocating for justice.
• It explores how language influences power structures, societal norms, and perceptions that can either promote equality or reinforce injustice.
• The book delves into the importance of inclusive and non-discriminatory language in creating equitable societies.
• It emphasizes the responsibility of policymakers, educators, and individuals to use language in ways that empower marginalized communities.
• Through examples and case studies, the book demonstrates how thoughtful language can lead to constructive social change and justice-driven narratives.

Additional Information

• Ancient Sanskrit grammar
• Sanskrit grammar is one of the oldest linguistic systems, meticulously codified by Panini in his work "Ashtadhyayi."
• It provides insights into the structure and phonetics of the Sanskrit language, forming the basis of modern linguistic studies.
• While significant, the topic of ancient Sanskrit grammar does not align with the theme of social justice discussed in "Because Words Matter."
• Novel on colonial India
• Colonial literature often explores themes of oppression, cultural conflict, and the impact of British rule on Indian society.
• Such novels typically focus on historical narratives rather than the impact of language on societal structures.
• "Because Words Matter" does not fall under this category as it addresses the broader implications of language in social justice contexts.
• Linguist's critique of post-colonial English
• Post-colonial English studies analyze how language evolved in former colonies under British influence.
• It examines how colonial powers imposed their linguistic norms, often suppressing indigenous languages and cultures.
• Although the critique of post-colonial English intersects with language studies, "Because Words Matter" focuses on broader issues of social justice rather than this specific area.

The correct answer is It affects material to considerable depth.

Key Points

• Rockslides are a form of mass wasting, characterized by the downslope movement of rock material along a bedding plane, fracture, or other structural weakness.
• Unlike rockfalls, rockslides involve the sliding of large masses of rock, which often penetrates to significant depths within the geological formation.
• The movement of rock material during a rockslide is typically more cohesive and affects a considerable volume of rock in a single event.
• Rockslides are often triggered by natural phenomena such as earthquakes, heavy rainfall, volcanic activities, or human activities like mining and construction.
• They can lead to significant changes in the landscape, often causing widespread destruction and posing risks to life and infrastructure.

Additional Information

• Mass Wasting
• Mass wasting refers to the downslope movement of earth materials under the influence of gravity.
• It includes various processes such as rockfalls, rockslides, slumping, and debris flows.
• Understanding mass wasting is crucial for mitigating risks in areas prone to landslides, earthquakes, and other geological hazards.

The correct answer is He won with his opening throw of 88.16m at Stade Sébastien Charléty..

Key Points

• Neeraj Chopra secured victory at the Paris Diamond League 2025 with his opening throw of 88.16 meters at Stade Sébastien Charléty.
• This outstanding throw placed him at the top of the leaderboard, cementing his dominance in javelin throwing on the global stage.
• The Paris Diamond League is a prestigious athletics competition that attracts top athletes from around the world.
• Neeraj Chopra's consistent performance and ability to excel under pressure highlight his expertise as an Olympic gold medalist and world-class javelin thrower.
• He continues to be a source of pride for India, showcasing his extraordinary talent in international competitions.

Additional Information

• Neeraj Chopra’s major International Medals:
• Olympic Games: Gold (Tokyo 2020), Silver (Paris 2024).
• World Athletics Championships: Gold (Budapest 2023), Silver (2022).
• Asian Games: Gold (Jakarta 2018, Hangzhou 2023).
• Commonwealth Games: Gold (Gold Coast 2018).
• Diamond League: Wins and podium finishes, including breaking national records.

The correct answer is V. Narayanan.

Key Points

• Dr. V. Narayanan is a distinguished scientist at ISRO and has played a crucial role in India's space programs, especially in the domain of rocket propulsion.
• He succeeded S. Somanath as the Chairman of ISRO and Secretary of the Department of Space in January 2025.
• Dr. Narayanan has been instrumental in the development of cryogenic propulsion systems, including the Cryogenic Upper Stage (CUS) for the GSLV rocket.
• He led the Liquid Propulsion Systems Centre (LPSC), which is a vital division of ISRO responsible for the development of liquid propulsion technologies.
• Under his leadership, ISRO has achieved significant advancements in rocket technologies and launched several impactful missions.

Additional Information

• K. Radhakrishnan
• Dr. K. Radhakrishnan is a former Chairman of ISRO who served from 2009 to 2014.
• He was instrumental in the successful launch of the Mars Orbiter Mission (Mangalyaan) in 2013, making India the first country to reach Mars in its maiden attempt.
• He was honored with the Padma Bhushan in 2014 for his contributions to space science and technology.
• K. Sivan
• Dr. K. Sivan served as the Chairman of ISRO from January 2018 to January 2022.
• He played a key role in launching Chandrayaan-2 and several other satellite missions during his tenure.
• Dr. Sivan is well-known for his work in designing and developing the PSLV project.
• S. Sashidhar Sinha
• S. Sashidhar Sinha is not associated with ISRO leadership roles or space technology advancements.
• This option is irrelevant to the context of ISRO Chairman appointments.

The correct answer is Option 2.

Key Points

• Statement 2: Spillways in dams are structures designed to regulate the water flow from the dam, ensuring safety by preventing overflow or damage during high inflow periods.
• Spillways can be operated either intermittently during periods of excess water inflow or continuously for controlled discharge, depending on the dam’s design and requirements.
• Statement 3: Dams are classified based on various factors such as structure (e.g., gravity dams, arch dams), purpose (e.g., irrigation, hydroelectricity, flood control), and height (e.g., low, medium, or high dams).
• Both statements 2 and 3 are factually accurate and highlight the functional and classification aspects of dams.

Additional Information

• Spillways:
• Spillways are integral safety features of dams used to release excess water when the reservoir reaches its capacity.
• Types of spillways include gated spillways, ogee spillways, and chute spillways, among others.
• They help prevent overtopping, which could otherwise lead to the dam’s failure.
• Dams classification: Dams are categorized based on:
• Structure: Examples include gravity dams, arch dams, and embankment dams.
• Purpose: Common purposes include irrigation, hydroelectric power generation, water supply, and flood control.
• Height: Dams are classified as low dams (less than 15 meters), medium dams (15-30 meters), and high dams (above 30 meters).

The correct answer is Corona.

Key Points

• Aditya-L1 spacecraft is India’s first solar mission launched by the Indian Space Research Organisation (ISRO).
• The primary focus of Aditya-L1 is to study the Sun’s corona, which is the outermost layer of the Sun’s atmosphere.
• The corona is known for its extremely high temperature, which is much hotter than the Sun’s surface, reaching up to millions of degrees Celsius.
• The spacecraft is equipped with multiple scientific instruments, including the Visible Emission Line Coronagraph (VELC), to observe the corona and understand the mechanisms behind solar activity.
• Studying the corona helps scientists understand phenomena like solar flares, coronal mass ejections (CMEs), and their impact on space weather and Earth’s magnetosphere.

Additional Information

• Regolith:
• Regolith refers to the layer of loose, unconsolidated material covering solid rock, such as soil, dust, and broken rock.
• It is commonly studied in planetary science, particularly for celestial bodies like the Moon, Mars, and asteroids.
• Regolith is unrelated to the Sun, as it deals primarily with terrestrial or planetary surface materials.
• Craters:
• Craters are bowl-shaped depressions formed by the impact of meteorites or volcanic activity on solid surfaces such as planets, moons, or asteroids.
• They are not relevant to the study of the Sun, as the Sun does not have a solid surface to form craters.
• Magnetosphere:
• The magnetosphere is the region surrounding a planet, dominated by its magnetic field, which protects it from solar wind and cosmic radiation.
• Though the Sun’s magnetic field plays a key role in solar activity, Aditya-L1 primarily focuses on studying the corona rather than the magnetosphere.

The correct answer is Copper, Zinc, Lead.

Key Points

• Copper, zinc, and lead are classified as non-ferrous metallic minerals, which are metals that do not contain iron.
• India has limited reserves of these minerals, making them scarce in comparison to other metallic and non-metallic minerals.
• Copper is primarily used in electrical wiring, electronics, and alloys. India produces copper mainly in Rajasthan, Madhya Pradesh, and Jharkhand, but the production levels do not meet domestic demand.
• Zinc is used for galvanizing iron and steel to prevent rusting, as well as in alloys and chemical industries. Zinc reserves in India are concentrated in Rajasthan, but the production is insufficient for industrial requirements.
• Lead is used in batteries, shielding against radiation, and other industrial applications. Its reserves are also limited in India, mainly found in Rajasthan.

Additional Information

• Iron, Coal, Bauxite
• Iron is a ferrous metallic mineral widely found in India, particularly in Odisha, Jharkhand, Chhattisgarh, and Karnataka. It is used in the steel industry.
• Coal is a non-metallic mineral and serves as a major energy source. India is the second-largest producer of coal globally, with reserves in Jharkhand, Odisha, and Chhattisgarh.
• Bauxite is a non-metallic mineral and the primary ore for aluminum production. India has significant reserves of bauxite, especially in Odisha, Andhra Pradesh, and Maharashtra.
• Manganese, Limestone
• Manganese is a ferrous metallic mineral used in steel production and chemical industries. India is one of the leading producers of manganese globally, with deposits in Madhya Pradesh, Maharashtra, and Odisha.
• Bauxite, as stated earlier, is a non-metallic mineral primarily used for aluminum production.
• Limestone is a non-metallic mineral used in cement production and as a flux in steel manufacturing. It is abundantly found in India, particularly in Madhya Pradesh, Rajasthan, and Andhra Pradesh.
• Mica, Dolomite, Felspar
• Mica is a non-metallic mineral used in electrical and electronic industries for insulation. India is the largest producer of mica globally, with reserves in Andhra Pradesh, Rajasthan, and Jharkhand.
• Dolomite is a non-metallic mineral used in the steel, glass, and ceramic industries. It is found in Madhya Pradesh, Chhattisgarh, and Andhra Pradesh.
• Feldspar is a non-metallic mineral used in the glass and ceramic industries. It is widely found in Rajasthan and Tamil Nadu.

The correct answer is States Reorganisation Act, 1956.

Key Points

• The Zonal Councils in India were established under the States Reorganisation Act, 1956, which aimed to reorganize states based on linguistic and administrative considerations.
• The primary objective of Zonal Councils was to foster cooperation and coordination among states and Union Territories in a particular zone.
• There are five Zonal Councils—Northern, Central, Eastern, Western, and Southern—each comprising states grouped based on geographical proximity.
• The Zonal Councils are chaired by the Union Home Minister and include the Chief Ministers of the member states, along with other ministers as representatives.
• Zonal Councils serve as a platform to resolve inter-state disputes and promote regional development by addressing common issues such as economic planning, border disputes, and cultural exchanges.

Additional Information

• Finance Commission
• The Finance Commission is constituted under Article 280 of the Indian Constitution.
• It is primarily responsible for dividing tax revenues between the Central and State governments and addressing financial relations between them.
• The Finance Commission is appointed every five years, and its recommendations are advisory in nature.
• It does not pertain to the creation of Zonal Councils but plays a crucial role in managing fiscal matters in federal governance.
• Panchayati Raj
• The Panchayati Raj system was introduced as a form of decentralized governance under Article 40 of the Directive Principles of State Policy in the Constitution.
• The 73rd Constitutional Amendment Act, 1992, provided constitutional status to Panchayati Raj institutions.
• It focuses on grassroots-level governance and local self-government but does not relate to Zonal Councils.
• Representation of the People Act
• The Representation of the People Act, 1951, governs the conduct of elections in India.
• It provides provisions for the qualification and disqualification of Members of Parliament and State Legislatures.
• While it is critical in ensuring free and fair elections, it is unrelated to the establishment of Zonal Councils.

The correct answer is The Union Government can issue directions to the States under Article 256.

Key Points

• Article 256 of the Indian Constitution states that the executive power of every state is to be exercised in a way that ensures compliance with the laws made by the Parliament.
• The Union Government has the authority to issue directions to the states to ensure the implementation of such laws.
• This provision ensures the supremacy of parliamentary laws over state laws in case of conflict.
• Such directions issued by the Union are binding on the states, and non-compliance may result in consequences under Article 356 (President’s Rule).
• This mechanism ensures the cohesive functioning of the federal structure in India and maintains the unity and integrity of the country.

Additional Information

• Union Legislature (Parliament)
• Composition: President, Lok Sabha (House of the People), and Rajya Sabha (Council of States).
• Powers: Exclusive power over Union List, concurrent power over Concurrent List, with overriding power over states.
• Rajya Sabha: Indirectly elected, permanent house (not dissolved), one-third members retire every two years, 12 nominated members for arts/science.
• Lok Sabha: Directly elected, represents the people.
• State Legislature
• Composition: Varies; some bicameral (Assembly & Council), most unicameral (Assembly only).
• Powers: Exclusive power over State List, concurrent power over Concurrent List.
• Legislative Council (Upper House): Indirectly elected members from local authorities, graduates, teachers, MLAs, and nominated by Governor; permanent house, not dissolved, one-third retire every two years.
• Legislative Assembly (Lower House): Directly elected by people, members 40-500.

The correct answer is 1) Both A and R are true, and R is the correct explanation of A.

Key Points

• The PSLV-C59 mission, mentioned in Assertion (A), is projected to take place in October 2024, marking a significant milestone for international space cooperation.
• Reason (R) highlights the deployment of Proba-3 satellites, which are part of the European Space Agency’s (ESA) innovative formation-flying experiment.
• Proba-3 is designed to demonstrate precise satellite positioning in orbit, enabling scientific experiments such as solar coronagraphy.
• The connection between Assertion (A) and Reason (R) lies in the fact that the successful deployment of Proba-3 by PSLV-C59 exemplifies international collaboration and technological advancement.
• Hence, both Assertion and Reason are true, and Reason correctly explains Assertion.

Additional Information

• PSLV and Proba-3 
• PSLV (Polar Satellite Launch Vehicle) is India’s third-generation satellite launch vehicle, known for its reliability and versatility.
• Proba-3 is a pair of ESA satellites designed for formation-flying experiments, with applications in solar science and other advanced research areas.
• Such missions emphasize the importance of international collaboration in space exploration and technological advancements.

The correct answer is CCTNS.

Key Points

• Crime and Criminal Tracking Network and Systems (CCTNS) is a comprehensive and integrated system for effective policing through e-Governance.
• It was launched by the Ministry of Home Affairs (MHA), Government of India, in 2009 as part of the national e-governance initiative.
• CCTNS facilitates a nationwide networked infrastructure for tracking crime and criminals in real-time, ensuring seamless sharing of information between police stations and higher police authorities.
• The system also enables citizens to access police services such as lodging FIRs, tracking case status, and obtaining verification certificates online.
• As of now, most states and union territories in India use the CCTNS platform to provide services like digital filing of FIRs, improving transparency and efficiency in policing activities.

Additional Information

• National Crime Portal
• It is not a specific portal but often refers to platforms like the National Crime Records Bureau (NCRB) website.
• The NCRB is responsible for collecting and analyzing crime data as mandated by the Ministry of Home Affairs but does not directly allow citizens to lodge FIRs.
• BHAVISHYA
• BHAVISHYA is an online Pension Sanction and Payment Tracking System launched by the Government of India.
• It is designed to cater to retiring employees for tracking their pension process, ensuring transparency and timely disbursal.
• This portal is unrelated to crime or police services.
• DIGI-FIR
• DIGI-FIR is a concept introduced in some states like Madhya Pradesh to allow citizens to lodge FIRs online.
• While it serves a similar purpose, it is not implemented nationwide or as comprehensively as CCTNS.
• Bharatiya Nagarik Suraksha Samhita (BNSS)
• The BNSS is a proposed draft legislation aimed at replacing the existing Code of Criminal Procedure (CrPC) to modernize and streamline the criminal justice system in India.
• One of its key features is enabling citizens to access FIRs and other police services online, which aligns with the goals of CCTNS.

The correct answer is e-NAM - Ministry of Agriculture & Farmers Welfare.

Key Points

• e-NAM (National Agriculture Market) is an online trading platform developed to create a unified national market for agricultural commodities.
• It is spearheaded by the Ministry of Agriculture & Farmers Welfare, aiming to connect farmers, traders, and buyers digitally.
• e-NAM was launched by the Government of India on 14th April 2016 as a major step towards agricultural reforms.
• The platform facilitates better price discovery through transparent auction processes and eliminates intermediaries, benefiting farmers directly.
• As of October 2023, e-NAM has integrated over 1,000 mandis across India, enhancing the efficiency of agricultural marketing.

Additional Information

• PM-AASHA - Ministry of Consumer Affairs, Food & Public Distribution
• PM-AASHA (Pradhan Mantri Annadata Aay Sanrakshan Abhiyan) is a scheme launched in 2018 aimed at ensuring remunerative prices for farmers' produce.
• It comprises three components: Price Support Scheme (PSS), Price Deficiency Payment Scheme (PDPS), and Pilot of Private Procurement and Stockist Scheme (PPPS).
• However, the nodal ministry for PM-AASHA is the Ministry of Agriculture & Farmers Welfare, not the Ministry of Consumer Affairs, Food & Public Distribution.
• PMKSY - Ministry of Water Resources, River Development & Ganga Rejuvenation
• Pradhan Mantri Krishi Sinchayee Yojana (PMKSY) aims to improve irrigation efficiency and increase agricultural productivity.
• The nodal ministry for PMKSY is the Ministry of Agriculture & Farmers Welfare, not the Ministry of Water Resources.
• It includes components such as Accelerated Irrigation Benefit Programme (AIBP) and Har Khet Ko Pani.
• RODTEP - Ministry of Finance
• Remission of Duties and Taxes on Exported Products (RODTEP) is a scheme launched in January 2021 to boost exports by reimbursing taxes and duties incurred during manufacturing and transport.
• The nodal ministry for RODTEP is the Ministry of Commerce and Industry, not the Ministry of Finance.
• It replaced the earlier MEIS (Merchandise Exports from India Scheme) to align with World Trade Organization (WTO) rules.

The correct answer is Guru Ghasidas.

Key Points

• Panthi dance is a traditional folk dance form closely associated with the followers of Guru Ghasidas in Chhattisgarh.
• It is performed as a devotional tribute to Guru Ghasidas, who founded the Satnami sect, emphasizing equality, truth, and social justice.
• The dance is characterized by spiritual songs and rhythmic movements, portraying the teachings of Guru Ghasidas and the values of the Satnami sect.
• Panthi dance holds great cultural significance in Chhattisgarh, particularly during festive occasions such as Maghi Purnima, which marks the birth anniversary of Guru Ghasidas.
• The performers use expressive gestures, devotional hymns, and synchronized movements to narrate stories of Guru Ghasidas' life and his efforts to promote social harmony.

Additional Information

• Kabir
• Kabir was a 15th-century Indian mystic poet and saint whose teachings emphasized devotion to one God and rejected idol worship.
• He inspired the Kabir Panth, a religious movement based on his philosophy of universal love and unity.
• Kabir's poetry, including dohas (couplets), is widely studied for its spiritual depth and social relevance.
• Kabuli
• The term "Kabuli" generally refers to people or things originating from Kabul, Afghanistan.
• It is not directly related to any specific dance or cultural tradition in Chhattisgarh.
• Nanak
• Guru Nanak was the founder of Sikhism and the first Sikh Guru, whose teachings focused on equality, truth, and devotion to one God.
• His philosophy inspired the formation of a distinct religious community, and his hymns are included in the Guru Granth Sahib.

The correct answer is By diverting climate funds and allowing undue influence over environmental policies.

Key Points

• Corruption diverts funds allocated for climate change mitigation and adaptation projects, reducing their effectiveness and delaying critical climate action.
• By allowing undue influence over environmental policies, corrupt practices prioritize the interests of powerful corporations or individuals over the environment and public welfare.
• Mismanagement of climate funds can lead to inefficient or poorly executed projects, further exacerbating environmental degradation.
• Corruption undermines trust in public institutions and international climate agreements, discouraging investment and collaboration in environmental initiatives.
• According to Transparency International, corruption in environmental governance is a significant barrier to achieving global climate goals, as it weakens enforcement mechanisms and promotes unsustainable practices.

Additional Information

• Corruption and Global Climate Action
• Corruption poses a significant challenge to global efforts to combat climate change, as it weakens the governance and implementation of policies.
• Addressing corruption is crucial for ensuring the effective use of climate funds and achieving sustainable development goals (SDGs).
• Global initiatives, such as the Paris Agreement, emphasize the need for transparency and accountability in climate financing and governance.

The correct answer is Balance conservation and livelihoods.

Key Points

• India's new Eco-Tourism Policy aims to balance environmental conservation and sustainable livelihoods for local communities residing in protected areas.
• The policy promotes community-based tourism, involving local stakeholders to ensure their active participation and equitable benefit-sharing.
• It emphasizes responsible tourism practices that minimize negative ecological impacts while enhancing awareness about biodiversity conservation.
• Protected areas under this policy, including wildlife sanctuaries and national parks, will integrate sustainable economic activities to support local communities.
• The Eco-Tourism Policy aligns with India's National Biodiversity Action Plan and Sustainable Development Goals (SDGs), particularly SDG 15 (Life on Land) and SDG 8 (Decent Work and Economic Growth).

Additional Information

• Ban human activity
• Banning human activity entirely in protected areas is not feasible or practical as many local communities depend on these areas for their livelihoods.
• While certain activities like poaching and deforestation are prohibited, regulated human activity, such as eco-tourism, is encouraged to strike a balance between conservation and community needs.
• India's wildlife protection laws, including the Wildlife Protection Act 1972, allow for controlled human interaction to support conservation efforts.
• Maximize profit without community
• This approach contradicts the principles of sustainable and responsible tourism.
• Ignoring local communities in eco-tourism policies can lead to social unrest and environmental degradation.
• India's Eco-Tourism Policy emphasizes community involvement to ensure equitable distribution of benefits and preservation of ecological integrity.
• Turn areas into resorts
• Turning protected areas into resorts is against the principles of conservation and can lead to habitat destruction.
• Eco-tourism promotes low-impact accommodations, such as eco-lodges, rather than large-scale resorts.
• The policy strictly avoids commercialization and prioritizes preserving the natural environment.

The correct answer is Only 1, 2 and 4.

Key Points

• Sucrose content in sugarcane decreases during transportation: Sugarcane is highly perishable, and its sucrose content starts deteriorating if there is a delay in processing after harvesting. This makes timely transportation critical for the sugar industry.
• Seasonal nature of the sugar industry: Sugar production depends heavily on sugarcane harvest seasons, which makes the industry seasonal in nature. The crushing season typically occurs from October to March in India.
• Major sugar-producing states include Maharashtra and Tamil Nadu: Maharashtra is the largest sugar-producing state, followed by Uttar Pradesh, Karnataka, and Tamil Nadu. Favorable climatic conditions and irrigation facilities contribute to high sugarcane yields in these states.
• Cooperative management's role: The sugar industry in India thrives on the cooperative model, especially in states like Maharashtra. Farmers are often stakeholders in cooperative sugar mills, which helps in organizing small-scale producers and ensuring equitable returns.

Additional Information

• Key Sectors by Contribution & Growth:
• Information Technology & Services: A global powerhouse, especially in software, IT-enabled services (ITES), and digital infrastructure (e.g., IT/BPM, Fintech).
• Manufacturing:
• Automobile: India is a major global market and producer of vehicles and components.
• Textiles & Apparel: An ancient, large employer, crucial for exports.
• Pharmaceuticals & Biotech: A leading global supplier of generic medicines.
• Chemicals: Specialty chemicals and petrochemicals are growing.
• Core Industries: Steel, Cement, Electricity, Petroleum products, Coal, Crude Oil, Natural Gas, and Fertilizers are foundational.
• Agriculture & Food Processing: A massive sector supporting food security, with significant processing growth.
• Infrastructure: Includes Construction, Power, Ports, Roads, and related Engineering & Capital Goods.

The correct answer is Option 2: 1 and 3.

Key Points

• The MISHTI (Mangrove Initiative for Shoreline Habitats & Tangible Incomes) programme is designed to increase mangrove forest cover across India's coastal regions.
• This initiative aims to enhance livelihood opportunities for communities residing in coastal areas by promoting sustainable mangrove conservation.
• The programme is financed through a mix of funding sources, specifically from the CAMPA (Compensatory Afforestation Fund Management and Planning Authority) Fund and MGNREGS (Mahatma Gandhi National Rural Employment Guarantee Scheme).
• It aligns with India’s international commitments to combat climate change, such as the Nationally Determined Contributions (NDCs) under the Paris Agreement.
• Mangroves are critical ecosystems that protect shorelines from erosion, act as carbon sinks, and support biodiversity.

Additional Information

• CAMPA Fund
• The CAMPA Fund is a mechanism established to manage the money collected for compensatory afforestation in India.
• It is utilized to restore degraded ecosystems, including mangroves, to offset the ecological damage caused by deforestation for development projects.
• MGNREGS
• The Mahatma Gandhi National Rural Employment Guarantee Scheme (MGNREGS) is a rural employment programme providing 100 days of wage employment to rural households.
• Under the MISHTI initiative, MGNREGS is leveraged to provide livelihood opportunities for local communities engaged in mangrove plantation and conservation activities.

The correct answer is Only 1.

Key Points

• Kalbelia performers primarily pass down their art forms orally, which aligns with their nomadic traditions and cultural heritage.
• The Kalbelia dance and music are deeply tied to the community's identity, and the lack of documentation reflects their oral knowledge systems.
• The dance, performed by the women of the Kalbelia community, is inspired by the graceful movements of serpents.
• The Kalbelia art form was inscribed in the UNESCO Representative List of the Intangible Cultural Heritage of Humanity in 2010.
• The inclusion in the UNESCO list required formal documentation and an application process, which was facilitated by cultural organizations and not directly by the community.

Additional Information

• Kalbelia Community and Art
• The Kalbelia community is traditionally a nomadic tribe in Rajasthan, India, known for their association with snake-charming.
• Their dance and music reflect their traditional occupation of snake-catching and their deep cultural and spiritual connection to serpents.
• Kalbelia dance is characterized by intricate footwork, fluid body movements, and rhythmic music played with instruments like the pungi and dholak.
• The art form is a significant part of Rajasthan's cultural heritage and showcases the creativity and resilience of the Kalbelia community.

The correct answer is Option 1.

Key Points

• A Money Bill is a specific type of Financial Bill under Article 110 of the Indian Constitution.
• Every Money Bill is a Financial Bill because it contains provisions exclusively dealing with financial matters such as taxation, borrowing, expenditure, or other money-related issues.
• However, not every Financial Bill is a Money Bill. Financial Bills can also include provisions beyond the scope of Article 110, requiring approval from both Houses of Parliament.
• A Money Bill can only be introduced in the Lok Sabha and requires the certification of the Speaker of the Lok Sabha.
• Thus, Statement 1 is correct, and Statement 2 is incorrect, making Option 1 the correct answer.

Additional Information

• Money Bill:
• A Money Bill is defined under Article 110 of the Indian Constitution.
• It contains provisions exclusively related to taxes, borrowing of money by the government, withdrawal of money from the Consolidated Fund or Contingency Fund, and appropriation of funds.
• It must be introduced in the Lok Sabha with the recommendation of the President.
• The Rajya Sabha can suggest amendments but cannot amend or reject a Money Bill. It has to return the bill to the Lok Sabha within 14 days.
• Financial Bill:
• Financial Bills are broader in scope and include Money Bills as a subset. There are two types of Financial Bills:
• Category A: These contain provisions related to financial matters and provisions not covered under Article 110. They need the President's recommendation and must be introduced in the Lok Sabha.
• Category B: These involve only incidental financial provisions and do not require the President's recommendation.

Shortcut Trick

To find the compound ratio N : P directly, we can multiply the given intermediate ratios N : O and O : P.

N / P = (N / O) × (O / P)

N / P = (6 / 7) × (9 / 11)

N / P = 54 / 77

∴ The correct answer is 54 : 77.

Alternate Method

Given:

M : N = 4 : 5

N : O = 6 : 7

O : P = 9 : 11

N O P

6 7 → 7

9 ← 9 11

54 63 77

Calculations:

⇒ To find the combined ratio, make the common term (O) equal in both ratios by taking the LCM of 7 and 9, which is 63.

⇒ Multiply the N : O ratio by 9 ⇒ N : O = (6 × 9) : (7 × 9) = 54 : 63

⇒ Multiply the O : P ratio by 7 ⇒ O : P = (9 × 7) : (11 × 7) = 63 : 77

⇒ Now, the combined ratio N : O : P = 54 : 63 : 77

⇒ Extracting the required values N and P from the combined ratio, we get N : P = 54 : 77

(Note: M : N is extraneous information and is not required for solving the problem.)

∴ The correct answer is 54 : 77.

Additional Information

Compound Ratio

When two or more ratios are multiplied together, the resulting ratio is called a compound ratio. For a : b and c : d, the compound ratio is ac : bd.

Combining Ratios

If A : B = x : y and B : C = p : q, you can combine them by equating the common term 'B'. Multiply the first ratio by p and the second by y to get A : B : C = xp : yp : yq.

Extraneous Data in Exams

Questions often contain additional data (like M : N in this problem) that is not required to find the final answer. Reading the question carefully to identify the core requirement saves valuable exam time.

Shortcut Trick

Convert the mixed fraction directly to a decimal: 2¹/₄ = 2.25

Dividing any number by 0.5 is mathematically equivalent to multiplying that number by 2.

⇒ 2.25 × 2 = 4.5

∴ The correct answer is 4.5.

Alternate Method

Given:

Expression: 2¹/₄ ÷ 0.5

Calculations:

⇒ Convert the mixed fraction into an improper fraction:

⇒ 2¹/₄ = (2 × 4 + 1) / 4 = 9/4

⇒ Convert the decimal 0.5 into a fraction:

⇒ 0.5 = 5/10 = 1/2

⇒ Substitute the fractions into the given expression:

⇒ 9/4 ÷ 1/2

⇒ To divide by a fraction, multiply by its reciprocal:

⇒ 9/4 × 2/1

⇒ Multiply the numerators and denominators:

⇒ 18/4

⇒ Simplify the resulting fraction:

⇒ 9/2 = 4.5

∴ The correct answer is 4.5.

Additional Information

Fraction Division Rule

To divide by a fraction, multiply the first number by the reciprocal of the second fraction: (a/b) ÷ (c/d) = (a/b) × (d/c).

Mixed Fraction to Improper Fraction

Multiply the whole number part by the denominator, add the numerator, and place the result over the original denominator.

Decimal to Fraction Conversion

Decimals can be easily converted to fractions by placing the number over its place value (e.g., 0.5 = 5/10 = 1/2, or 0.25 = 25/100 = 1/4).

Shortcut Trick

Let the given numbers be a = 10, b = 12, c = 13, and d = 16.

Direct formula for the number to be subtracted: x = (a × d − b × c) ÷ ((a + d) − (b + c))

⇒ x = (10 × 16 − 12 × 13) ÷ ((10 + 16) − (12 + 13))

⇒ x = (160 − 156) ÷ (26 − 25)

⇒ x = 4 ÷ 1 = 4

∴ The correct answer is 4.

Alternate Method

Given:

The numbers are 10, 12, 13, and 16.

Let the number to be subtracted from each term be x.

Formula Used:

If four numbers A, B, C, and D are in proportion, then A : B :: C : D or A ÷ B = C ÷ D.

10 − x

12 − x

=

13 − x

16 − x

Proportion: (10 − x) : (12 − x) :: (13 − x) : (16 − x)

Calculations:

⇒ (10 − x) ÷ (12 − x) = (13 − x) ÷ (16 − x)

⇒ Cross-multiplying both the sides:

⇒ (10 − x) × (16 − x) = (13 − x) × (12 − x)

⇒ 160 − 10x − 16x + x² = 156 − 13x − 12x + x²

⇒ 160 − 26x = 156 − 25x

⇒ 26x − 25x = 160 − 156

⇒ x = 4

∴ The correct answer is 4.

Additional Information

Fourth Proportional

If a, b, c, and d are in proportion (a : b :: c : d), then d is called the fourth proportional. It is calculated as d = (b × c) ÷ a.

Third Proportional

For two numbers a and b, the third proportional c is defined such that a : b :: b : c. It is calculated as c = b² ÷ a.

Mean Proportional

The mean proportional between two positive numbers a and b is given by √(a × b). It represents the middle term in a continuous proportion.

Componendo and Dividendo Rule

If a ÷ b = c ÷ d, then according to this mathematical rule: (a + b) ÷ (a − b) = (c + d) ÷ (c − d).

Shortcut Trick

Difference in percentage = 45% − 30% = 15%

Value of 15% of the number = 0.9

1% of the number = 0.9 ÷ 15 = 0.06

100% of the number = 0.06 × 100 = 6

∴ The correct answer is 6.

Alternate Method

Given:

45% of a number is 0.9 more than 30% of it.

30% 15%

0.9 Difference

55%

Total = 100% = x

Calculations:

Let the number be x.

⇒ 45% of x − 30% of x = 0.9

⇒ (45 − 30)% of x = 0.9

⇒ 15% of x = 0.9

⇒ (15 ÷ 100) × x = 0.9

⇒ x = 0.9 × (100 ÷ 15)

⇒ x = 90 ÷ 15

⇒ x = 6

∴ The correct answer is 6.

Additional Information

Percentage Difference

When comparing two percentages of the same base value, the difference between their absolute values is equal to the percentage of the difference applied to the base. Formula: a% of x − b% of x = (a − b)% of x.

Base of Percentage

A percentage is always calculated on a base value (considered as 100%). Finding the unknown base given a percentage value involves multiplying the value by 100 and dividing by the given percentage.

Percentage to Fraction Conversion

To convert a percentage into a fraction, divide the value by 100. For example, 15% is equivalent to 15 ÷ 100 or 3 ÷ 20 in simplified fractional form.

Shortcut Trick

In partnership, Profit Ratio = Ratio of (Investment × Time).

Working in terms of thousands (k) to simplify calculations:

Sohan's effective capital = (90 × 8) + (60 × 4) = 720 + 240 = 960

Rohan's effective capital = 150 × 7 = 1050

Profit Ratio = 960 : 1050 = 96 : 105 = 32 : 35

∴ The correct answer is 32:35.

Alternate Method

Given:

Sohan's initial investment = ₹90,000

Time for which Sohan invested his initial amount = 5 + 3 = 8 months

Amount withdrawn by Sohan after 8 months = ₹30,000

Remaining time for Sohan's adjusted investment = 12 − 8 = 4 months

Rohan's investment = ₹1,50,000

Rohan joined after 5 months, so his investment time = 12 − 5 = 7 months

Formula Used:

Profit Ratio = (Investment₁ × Time₁) : (Investment₂ × Time₂)

0m 5m 8m 12m

Sohan

₹90k × 8m

₹60k × 4m

Rohan

₹150k × 7m

Effective Capital = Investment × Time

Calculations:

⇒ Sohan's remaining investment after withdrawal = 90,000 − 30,000 = ₹60,000

⇒ Sohan's effective capital = (90,000 × 8) + (60,000 × 4)

⇒ Sohan's effective capital = 7,20,000 + 2,40,000 = 9,60,000

⇒ Rohan's effective capital = 1,50,000 × 7 = 10,50,000

⇒ Profit Ratio (Sohan : Rohan) = 9,60,000 : 10,50,000

⇒ Ratio = 96 : 105

Dividing both sides by 3:

⇒ Ratio = 32 : 35

∴ The correct answer is 32:35.

Additional Information

Partnership Profit Sharing

Profit is shared among partners strictly based on their effective capital. The effective capital is calculated as the product of the capital invested and the time duration of the investment.

Compound Partnership

When partners invest for varying time intervals, or they alter (add/withdraw) their invested capital mid-way through the business term, it represents a compound partnership. The total effective capital is the sum of (capital × time) for each sub-period.

Working vs Sleeping Partner

A working partner actively manages the business and frequently takes a specified salary or percentage of the profit before the remainder is divided. A sleeping partner simply invests funds without engaging in day-to-day operations and receives only their proportionate share.

Shortcut Trick

Convert all animals to equivalent cows based on eating capacity: 1 horse = 2 cows, 1 sheep = 0.5 cows.

A's grazing = 18 horses × 4 months = (18 × 2) × 4 = 144 cow-months.

B's grazing = (24 cows × 6 months) + (36 sheep × 4 months) = 144 + (36 × 0.5) × 4 = 216 cow-months.

A's rent share = A's grazing ÷ Total grazing = 144 ÷ (144 + 216) = 144 ÷ 360 = 2/5.

∴ The correct answer is 2/5.

Alternate Method

Given:

A grazes 18 horses for 4 months.

B grazes 24 cows for 6 months and 36 sheep for 4 months.

Equivalence: 3 horses = 6 cows ⇒ 1 horse = 2 cows.

Equivalence: 4 cows = 8 sheep ⇒ 1 sheep = 0.5 cows.

Formula Used:

Rent Share = Individual Grazing Units ÷ Total Grazing Units

Grazing Units = Equivalent Number of Animals × Grazing Time

A: 144 units B: 216 units Total Grazing Equivalent = 360 Units

A's Rent Share = 144 ÷ 360 = 2/5

Calculations:

⇒ Convert A's animals to equivalent cows: 18 horses = 36 cows.

⇒ A's grazing units = 36 cows × 4 months = 144 cow-months.

⇒ Convert B's animals to equivalent cows: 36 sheep = 18 cows.

⇒ B's grazing units = (24 cows × 6 months) + (18 cows × 4 months).

⇒ B's grazing units = 144 + 72 = 216 cow-months.

⇒ Total grazing units = A's units + B's units = 144 + 216 = 360 cow-months.

⇒ A's fraction of the rent = 144 ÷ 360 = 2/5.

∴ The correct answer is 2/5.

Additional Information

Partnership with Proportional Usage

When resources are shared, rent or profit is divided based on the product of the quantity of usage and time: Profit Ratio = (Quantity₁ × Time₁) : (Quantity₂ × Time₂).

Base Conversion in Ratios

To accurately compare different types of assets (like varying animals), they must be converted into a common base unit using an equivalence ratio before summing up the values.

Compound Proportions

When a share depends on multiple factors (such as number of animals and duration of months), the compound ratio is the product of the simple ratios of those respective factors.

Shortcut Trick

Let the initial investments of X, Y, and Z be 2, 3, and 5 units respectively.

Profit ratio is directly proportional to the product of Investment × Time.

X's share = 2 × 18 = 36

Y's share = (3 × 6) + (1.5 × 12) = 18 + 18 = 36

Z's share = (5 × 3) + (3 × 15) = 15 + 45 = 60

Ratio of profit shares = 36 : 36 : 60 ⇒ 3 : 3 : 5.

∴ The correct answer is 3:3:5.

Alternate Method

Given:

Ratio of initial capitals of X, Y, and Z = 2 : 3 : 5

Total duration of the business = 18 months

After 3 months, Z withdrew 40% of his capital.

After another 3 months (i.e., after 6 months total), Y withdrew half of his capital.

Total profit = ₹3,24,000 (not required to find the ratio)

Formula Used:

Profit Ratio = (C₁ × T₁) : (C₂ × T₂) : (C₃ × T₃)

2 units × 18 months

3 × 6m 1.5 × 12m

5×3m 3 × 15m

X Y Z

= 36 = 36 = 60

Calculations:

⇒ Let the initial capitals of X, Y, and Z be 2x, 3x, and 5x respectively.

⇒ X invested 2x for the entire duration of 18 months.

⇒ X's equivalent capital = 2x × 18 = 36x

⇒ Y invested 3x for 6 months. He then withdrew half (1.5x) for the remaining 12 months.

⇒ Y's equivalent capital = (3x × 6) + (1.5x × 12) = 18x + 18x = 36x

⇒ Z invested 5x for 3 months. He then withdrew 40% (2x) leaving 3x for the remaining 15 months.

⇒ Z's equivalent capital = (5x × 3) + (3x × 15) = 15x + 45x = 60x

⇒ Ratio of profit shares of X : Y : Z = 36x : 36x : 60x

⇒ Dividing by the common factor of 12x, we get the ratio as 3 : 3 : 5.

∴ The correct answer is 3:3:5.

Additional Information

Partnership Profit Ratio

The profit is distributed among partners in the ratio of the product of their capital and the time period for which it is invested: Profit Ratio = (C₁ × T₁) : (C₂ × T₂).

Variable Investments

When a partner adds or withdraws capital mid-way, their total effective capital is calculated as the sum of the varying capital amounts multiplied by their respective time durations.

Sleeping vs Active Partner

An active partner may receive a fixed salary or a certain percentage of the total profit for managing the business before the remaining profit is distributed as per the capital-time ratio.

Shortcut Trick

Age of new student = Old Average + (New Total Members × Increase in Average)

Old Average = 16 years

New Total Members = 40 + 1 = 41 students

Increase in Average = 0.2 years

Age of new student = 16 + (41 × 0.2) = 16 + 8.2 = 24.2 years

∴ The correct answer is 24.2 years.

Alternate Method

Given:

⇒ Average age of 40 students = 16 years

⇒ Increase in average age = 0.2 years

Formula Used:

⇒ Total Age = Number of Students × Average Age

⇒ Age of New Student = Total age of new group − Total age of old group

40 Students Average = 16

1 New Student Age = x

41 Students (Total) New Average = 16.2 (+0.2)

Calculations:

⇒ Total age of 40 students = 40 × 16 = 640 years

⇒ Total students after admission = 40 + 1 = 41

⇒ New average age = 16 + 0.2 = 16.2 years

⇒ Total age of 41 students = 41 × 16.2 = 664.2 years

⇒ Age of the new student = 664.2 − 640 = 24.2 years

∴ The correct answer is 24.2 years.

Additional Information

1. Weighted Average

When combining two different groups, the overall combined average is calculated as A = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

2. Replacement in Average

If an existing person is replaced by a new person and the average changes, the value of the new person = Value of removed person + (Total members × Change in average).

3. Person Leaving a Group

When a person leaves the group, their age/value can be found directly by: Value = Old Average − (Remaining Members × Change in average).

Shortcut Trick

Supervisor's salary is ₹10,000 more than the group average (₹25,000 − ₹15,000).

When excluded, this ₹10,000 deficit is shared equally among the remaining 8 employees.

Decrease in their average = 10,000 ÷ 8 = ₹1,250

New average of 8 employees = 15,000 − 1,250 = ₹13,750

∴ The correct answer is ₹13,750.

Alternate Method

Given:

Total number of people = 8 employees + 1 supervisor = 9

Monthly average salary of 9 people = ₹15,000

Supervisor's salary = ₹25,000

Formula Used:

Total Value = Average × Number of Items

8 Employees 1 Sup.

Total = ₹1,10,000 ₹25,000

Total Salary of 9 = 9 × ₹15,000 = ₹1,35,000

Calculations:

⇒ Total salary of all 9 people = 9 × 15,000 = ₹1,35,000

⇒ Total salary of 8 employees = Total salary of 9 people − Supervisor's salary

⇒ Total salary of 8 employees = 1,35,000 − 25,000 = ₹1,10,000

⇒ Average salary of 8 employees = 1,10,000 ÷ 8

⇒ Average salary of 8 employees = ₹13,750

∴ The correct answer is ₹13,750.

Additional Information

Exclusion in Averages

When a value is removed from a group, the new average is calculated directly as: New Average = Old Average − [ (Value of Excluded Item − Old Average) ÷ Remaining Number of Items ].

Weighted Average

Used when combining two groups of varying sizes and averages: Combined Average = (n₁x₁ + n₂x₂) ÷ (n₁ + n₂).

Net Deviation Method

The sum of all deviations from the true average is always zero. Adding an item greater than the average increases the overall average, while removing it decreases the average.

Shortcut Trick

Ratio of women to men = 35% : 65% = 7 : 13

Let the base average be the men's average = 68 (in thousands).

Deviation of women's average from base = 72 − 68 = +4

Net change in overall average = (+4 × 7) ÷ (7 + 13) = +28 ÷ 20 = +1.4

Overall average = 68 + 1.4 = 69.4

∴ The correct answer is 69.4 (in ₹1000).

Alternate Method

Given:

Total employees = 80

Percentage of women = 35%

Average monthly salary of women = 72 (in ₹1000)

Average monthly salary of men = 68 (in ₹1000)

Formula Used:

Overall Average = (Total sum of salaries) ÷ (Total number of employees)

Men (68)Women (72)Avg (69.4)7 parts13 partsWeight: 13Weight: 7

Calculations:

⇒ Number of women = 35% of 80 = 28

⇒ Number of men = 80 − 28 = 52

⇒ Total salary of women = 28 × 72 = 2016 (in ₹1000)

⇒ Total salary of men = 52 × 68 = 3536 (in ₹1000)

⇒ Total salary of all employees = 2016 + 3536 = 5552 (in ₹1000)

⇒ Overall average salary = 5552 ÷ 80 = 69.4

∴ The correct answer is 69.4 (in ₹1000).

Additional Information

Weighted Average

When two groups of sizes n₁ and n₂ have individual averages x₁ and x₂, the combined group average is computed using the formula: (n₁x₁ + n₂x₂) ÷ (n₁ + n₂).

Deviation Method for Averages

To simplify calculations without multiplying large numbers, assume a base average. Determine the total surplus or deficit relative to this base, divide it evenly among all items, and adjust the base average accordingly.

Rule of Alligation

It establishes the ratio in which two components of different values must be combined to yield a specific average value. The ratio is derived as (Dearer Value − Mean Value) : (Mean Value − Cheaper Value).

Shortcut Trick

Difference in discount percentages = 15% − 10% = 5%

Extra discount amount is simply 5% of the Marked Price.

Extra discount = (5 ÷ 100) × 3500 = 175

∴ The correct answer is ₹175.

Alternate Method

Given:

Marked Price (MP) = ₹3,500

Initial Discount = 10%

New Discount = 15%

MP = ₹3500

10% = ₹350

15% = ₹525

Extra Discount = 5% = ₹175

Formula Used:

Discount Value = (Discount % ÷ 100) × MP

Extra Discount = New Discount Value − Initial Discount Value

Calculations:

⇒ Initial Discount Value = (10 ÷ 100) × 3500

⇒ Initial Discount Value = ₹350

⇒ New Discount Value = (15 ÷ 100) × 3500

⇒ New Discount Value = ₹525

⇒ Extra Discount = 525 − 350

⇒ Extra Discount = ₹175

∴ The correct answer is ₹175.

Additional Information

Marked Price vs Selling Price

Selling Price (SP) is obtained after applying the discount on the Marked Price. Formula: SP = MP − Discount.

Successive Discounts

When two discounts d₁% and d₂% are given consecutively, the single effective discount percentage is given by: d₁ + d₂ − (d₁ × d₂) ÷ 100.

Markup Percentage

The percentage by which the Marked Price is increased over the Cost Price. Markup % = ((MP − CP) ÷ CP) × 100.

Shortcut Trick

Let ordinary coffee price = 1 unit, premium = 3 units, and original ordinary quantity = x kg.

Original bill = (5 × 3) + (x × 1) = 15 + x

Swapped bill = (x × 3) + (5 × 1) = 3x + 5

Bill increased by 40%, meaning New Bill ÷ Old Bill = 140% = 7 / 5

⇒ (3x + 5) / (15 + x) = 7 / 5 ⇒ 15x + 25 = 105 + 7x ⇒ 8x = 80 ⇒ x = 10 kg

∴ The correct answer is 1 : 2.

Alternate Method

Original OrderPremium: 5 kg × 3POrdinary: x kg × 1PTotal: P(15 + x)+40% BillSwapped OrderPremium: x kg × 3POrdinary: 5 kg × 1PTotal: P(3x + 5)New Bill = 1.4 × Original Bill

Given:

Original quantity of premium coffee = 5 kg

Price of premium coffee = 3 × Price of ordinary coffee

Bill increased by 40% after swapping quantities.

Formula Used:

Total Value = (Quantity₁ × Price₁) + (Quantity₂ × Price₂)

Calculation:

⇒ Let the original quantity of ordinary coffee = x kg

⇒ Let the price of ordinary coffee = ₹P per kg

⇒ Then, the price of premium coffee = ₹3P per kg

⇒ Original Bill = (5 × 3P) + (x × P) = P(15 + x)

⇒ After swapping, quantity of premium coffee = x kg

⇒ Quantity of ordinary coffee = 5 kg

⇒ New Bill = (x × 3P) + (5 × P) = P(3x + 5)

⇒ The new bill is 40% more than the original bill.

⇒ New Bill = 1.4 × Original Bill

⇒ P(3x + 5) = 1.4 × P(15 + x)

⇒ 3x + 5 = 21 + 1.4x

⇒ 3x − 1.4x = 21 − 5

⇒ 1.6x = 16

⇒ x = 10 kg

⇒ Ratio of premium to ordinary coffee = 5 : 10 = 1 : 2

∴ The correct answer is 1 : 2.

Additional Information

Percentage Increase

If a value increases by R%, the new value becomes (1 + R/100) × Original Value. A 40% increase means the multiplier is 1.4 or 140/100 = 7/5.

Ratio & Proportion

A ratio indicates how many times one number contains another. The ratio a : b can also be expressed as the fraction a/b. Simplifying ratios involves dividing both terms by their highest common factor (HCF).

Mixtures & Total Value

When combining multiple items, the total value is the sum of the product of quantity and unit price for each item. Total Value = (Quantity₁ × Price₁) + (Quantity₂ × Price₂).

Shortcut Trick

For Compound Interest, the amount at the end of a year acts as the principal for the very next year.

Interest for the 3rd year = A₃ − A₂ = 7040 − 6400 = ₹640

Rate % = (Interest ÷ Principal) × 100

Rate % = (640 ÷ 6400) × 100 = 10%

∴ The correct answer is 10%.

Alternate Method

Given:

Amount after 2 years (A₂) = ₹6400

Amount after 3 years (A₃) = ₹7040

(Note: Based on the given options, the interest is compounded annually)

Formula Used:

A = P(1 + R/100)ⁿ

 Year 0 Year 2 Year 3 Principal ₹6400 ₹7040     + ₹640 (1 Year Interest) Rate = (640 ÷ 6400) × 100 = 10%

Calculations:

⇒ For 2 years: 6400 = P(1 + R/100)² --- (Equation 1)

⇒ For 3 years: 7040 = P(1 + R/100)³ --- (Equation 2)

⇒ Dividing Equation 2 by Equation 1:

⇒ 7040 ÷ 6400 = [P(1 + R/100)³] ÷ [P(1 + R/100)²]

⇒ 704 ÷ 640 = 1 + R/100

⇒ 1.1 = 1 + R/100

⇒ R/100 = 0.1

⇒ R = 10%

∴ The correct answer is 10%.

Additional Information

Compound Interest Successive Years

The amount at the end of any year acts as the principal for the very next year. Rate = [(A_n − A_n-1) ÷ A_n-1] × 100.

Simple Interest vs Compound Interest

For the first year, SI and CI are identical. From the second year onwards, CI earns interest on the accumulated interest, whereas SI is always calculated on the initial principal only.

Difference Between CI and SI

For 2 years, Difference = P(R/100)². For 3 years, Difference = P(R/100)² × (3 + R/100).

Shortcut Trick

The actual Selling Price (₹300) is not required to find the Loss %.

Let the Cost Price (CP) of 1 pen = 1 unit.

Total CP of 10 pens = 10 units.

Loss = CP of 4 pens = 4 units.

Loss % = (Loss ÷ Total CP) × 100 = (4 ÷ 10) × 100 = 40%.

∴ The correct answer is 40%.

Alternate Method

Given:

Selling Price (SP) of 10 pens = ₹300

Loss = Cost Price (CP) of 4 pens

Formula Used:

Loss = Total CP − Total SP

Loss % = (Loss ÷ Total CP) × 100

Total Cost Price (10 Pens) = ₹500

SP (10 Pens) = ₹300

Loss = ₹200 (Selling Amount) (CP of 4 pens) Loss % = (200 ÷ 500) × 100 = 40%

⇒ Let the Cost Price (CP) of 1 pen be ₹x.

⇒ Total CP of 10 pens = ₹10x

⇒ Loss = ₹4x

⇒ Since Loss = Total CP − Total SP

⇒ 4x = 10x − 300

⇒ 10x − 4x = 300

⇒ 6x = 300

⇒ x = 300 ÷ 6 = 50

⇒ Total CP of 10 pens = 10 × 50 = ₹500

⇒ Loss = 4 × 50 = ₹200

⇒ Loss % = (Loss ÷ Total CP) × 100

⇒ Loss % = (200 ÷ 500) × 100 = 40%

∴ The correct answer is 40%.

Additional Information

Profit and Loss Basics

Profit = SP − CP, and Loss = CP − SP. Both Profit % and Loss % are always calculated on the Cost Price (CP) unless specifically mentioned otherwise.

Direct Short-Trick Concept

If the loss on selling 'a' items equals the Cost Price of 'b' items, the Loss % = (b ÷ a) × 100 directly without needing the actual SP amount.

Marked Price & Discount

Discount is always offered on the Marked Price (MP). SP = MP − Discount. The equivalent discount of two successive discounts x% and y% is (x + y − x × y ÷ 100)%.

Shortcut Trick

Assume quantities identical to the ratio: 2, 3, and 1 (Total = 6 items).

Total CP = 2 × (10 ÷ 4) + 3 × (12 ÷ 5) + 1 × (5 ÷ 2) = 5 + 7.2 + 2.5 = ₹14.7

Total SP of 6 items = 6 × (7 ÷ 3) = ₹14.0

Loss = Total CP − Total SP = 14.7 − 14.0 = ₹0.7

Loss % = (0.7 ÷ 14.7) × 100 = (1 ÷ 21) × 100 ≈ 4.76%

∴ The correct answer is Loss of 4.76%.

Alternate Method

Given:

Buying price of 1st variety = 4 for ₹10

Buying price of 2nd variety = 5 for ₹12

Buying price of 3rd variety = 2 for ₹5

Ratio of the three varieties mixed = 2 : 3 : 1

Selling price of the mixture = 3 for ₹7

Formula Used:

Loss = Total CP − Total SP

Loss % = (Loss ÷ Total CP) × 100

Comparison of Cost and Selling Price

Total Cost Price (CP) = ₹14.7

Total Selling Price (SP) = ₹14.0

Loss = ₹0.7

₹14.7

Calculations:

⇒ Let the number of mangoes bought be 2, 3, and 1 respectively, making the total number of mangoes 6.

⇒ CP of 1st variety = 10 ÷ 4 = ₹2.5 per mango

⇒ CP of 2nd variety = 12 ÷ 5 = ₹2.4 per mango

⇒ CP of 3rd variety = 5 ÷ 2 = ₹2.5 per mango

⇒ Total CP = (2 × 2.5) + (3 × 2.4) + (1 × 2.5)

⇒ Total CP = 5 + 7.2 + 2.5 = ₹14.7

⇒ SP of 1 mixture mango = ₹(7 ÷ 3)

⇒ Total SP for all 6 mangoes = 6 × (7 ÷ 3) = ₹14.0

⇒ Since the Cost Price is greater than the Selling Price, there is an overall loss.

⇒ Loss = 14.7 − 14.0 = ₹0.7

⇒ Loss % = (0.7 ÷ 14.7) × 100

⇒ Loss % = (1 ÷ 21) × 100 ≈ 4.76%

∴ The correct answer is Loss of 4.76%.

Additional Information

Profit and Loss Fundamentals

A profit is realized when the Selling Price (SP) is greater than the Cost Price (CP). A loss occurs when the Cost Price is greater than the Selling Price.

Percentage Calculation Rule

Unless explicitly mentioned otherwise, both profit percentage and loss percentage are strictly computed relative to the Cost Price base: Percentage = (Value ÷ CP) × 100.

Weighted Mixtures Concept

When combining different quantities at varying rates, treating the given mixing ratio units as the actual physical quantity simplifies the arithmetic needed to evaluate the overall expenditure and returns.

Shortcut Trick

Let Cost Price (CP) = 100%.

Marked Price (MP) = 100% + 20% = 120%.

Selling Price (SP) = 120% − (15% of 120%) = 120% − 18% = 102%.

Profit = SP − CP = 102% − 100% = 2%.

Given, 2% = ₹300 ⇒ 100% = ₹15,000.

∴ The correct answer is ₹15,000.

Alternate Method

Given:

Markup = 20%

Discount = 15%

Profit = ₹300

Formula Used:

MP = CP × (100 + Markup%) ÷ 100

SP = MP × (100 − Discount%) ÷ 100

Profit = SP − CP

CP = 100xMP = 120xSP = 102x+20% Markup-15% DiscountProfit = 2x = ₹300

Calculations:

⇒ Let the Cost Price (CP) be 100x.

⇒ Marked Price (MP) = 100x × (100 + 20) ÷ 100 = 120x

⇒ Selling Price (SP) = 120x × (100 − 15) ÷ 100 = 120x × 85 ÷ 100 = 102x

⇒ Profit = 102x − 100x = 2x

⇒ 2x = 300

⇒ x = 150

⇒ CP = 100x = 100 × 150 = 15000

∴ The correct answer is ₹15,000.

Additional Information

Marked Price & Discount

Discount is always calculated on the Marked Price (MP). SP = MP × (100 − D%) ÷ 100.

Successive Discounts

If two successive discounts of a% and b% are given, the single equivalent discount is (a + b − a×b ÷ 100)%.

Relation between CP and MP

CP ÷ MP = (100 − Discount%) ÷ (100 + Profit%). This is a direct shortcut formula to find CP or MP without having to calculate SP.

Shortcut Trick Let Cost Price (CP) = 100 units ⇒ Marked Price (MP) = 100 + 25% = 125 units. Net discount = 10% + 20% − (10 × 20) ÷ 100 = 28%. Selling Price (SP) = 125 × (1 − 0.28) = 125 × 0.72 = 90 units. Loss = CP − SP = 100 − 90 = 10 units. 10 units = ₹400 ⇒ 1 unit = ₹40. MP = 125 units × 40 = ₹5000. ∴ The correct answer is ₹5000. Alternate Method Given: Markup = 25% above CP Consecutive discounts = 10% and 20% Loss = ₹400

CP = 100x

MP = 125x

SP = 90x

+25%

-10%, -20%

Loss = 100x − 90x = 10x 10x = ₹400 ⇒ x = 40

Calculations: Let the Cost Price (CP) of the article be 100x. ⇒ Marked Price (MP) = 100x + (25/100) × 100x = 125x Two consecutive discounts are given on the Marked Price: 10% and 20%. ⇒ Selling Price (SP) = MP × (100 − D1)/100 × (100 − D2)/100 ⇒ SP = 125x × (100 − 10)/100 × (100 − 20)/100 ⇒ SP = 125x × 0.90 × 0.80 ⇒ SP = 125x × 0.72 = 90x Loss is incurred when CP > SP. ⇒ Loss = CP − SP ⇒ Loss = 100x − 90x = 10x According to the given data, Loss = ₹400. ⇒ 10x = 400 ⇒ x = 40 Now, substitute the value of x to find the Marked Price: ⇒ MP = 125x = 125 × 40 = ₹5000 ∴ The correct answer is ₹5000. Additional Information Successive Discounts When two discounts d1% and d2% are given consecutively, the effective discount is: Net Discount = d1 + d2 − (d1 × d2) ÷ 100. Marked Price & Profit/Loss Marked price is the price printed on an article. Discount is always calculated on Marked Price (MP), while Profit or Loss is always calculated on Cost Price (CP). Single Equivalent Discount for 3 Discounts For three successive discounts a%, b% and c%, final SP = MP × (100 − a) ÷ 100 × (100 − b) ÷ 100 × (100 − c) ÷ 100.

Shortcut Trick

Let the remaining mixture (after removing 30 L) be 10x (since ratio is 3:5:2).

Quantities of P and Q in the remaining mixture are 3x and 5x respectively.

After adding 12 L of P and 8 L of Q, the difference is given as 20 L: (5x + 8) − (3x + 12) = 20.

⇒ 2x − 4 = 20 ⇒ x = 12.

Remaining mixture = 10 × 12 = 120 L. Initial total quantity = 120 + 30 = 150 L.

∴ The correct answer is 150 litres.

Alternate Method

Initial MixP:Q:R = 3:5:2− 30 LRemainingP=3x, Q=5x+12L P+8L QFinalP = 3x + 12Q = 5x + 8Given: Final Q − Final P = 20 L

Given:

Initial ratio of chemicals P, Q, and R = 3:5:2

Quantity of mixture removed = 30 litres

Quantity of P added = 12 litres

Quantity of Q added = 8 litres

Final amount of Q − Final amount of P = 20 litres

Calculations:

⇒ Let the remaining quantity of the mixture be 10x (since 3 + 5 + 2 = 10).

⇒ In the remaining mixture, quantity of P = 3x and quantity of Q = 5x.

⇒ After addition, resultant P = 3x + 12.

⇒ After addition, resultant Q = 5x + 8.

⇒ According to the given condition: Resultant Q − Resultant P = 20

⇒ (5x + 8) − (3x + 12) = 20

⇒ 2x − 4 = 20

⇒ 2x = 24 ⇒ x = 12

⇒ Remaining quantity of the mixture = 10x = 10 × 12 = 120 litres.

⇒ Initial total quantity = Remaining quantity + Removed quantity

⇒ Initial total quantity = 120 + 30 = 150 litres.

∴ The correct answer is 150 litres.

Additional Information

Mixture Replacement Rule

When a certain volume of a mixture is withdrawn, the ratio of the constituent elements in the remaining mixture remains exactly the same as in the original mixture.

Ratio & Proportion

If elements are present in the ratio a:b:c, their respective quantities can be assumed to be ax, bx, and cx, where the common multiplier 'x' represents a unit part of the total mixture.

Alligation Method

It is a general rule used to find the ratio in which two components of different concentrations are mixed to yield a desired concentration. The ratio of components is inversely proportional to the differences in their concentrations.

Shortcut Trick

Total effective interest rate = (3 × 5%) + (5 × 7%) + (2 × 9%)

⇒ Total rate = 15% + 35% + 18% = 68%

We are given that 68% of the total Principal = ₹6800

⇒ Principal (100%) = (6800 ÷ 68) × 100 = ₹10000

∴ The correct answer is ₹10000.

Alternate Method

Total Time = 10 Years

3 yrs @ 5% 15%

5 yrs @ 7% 35%

2 yrs @ 9% 18%

Total Interest = 15% + 35% + 18% = 68% 68% = ₹6800 → 100% = ₹10000

Given:

Rate for the first 3 years (R₁) = 5% per annum

Rate for the next 5 years (R₂) = 7% per annum

Total time given = 10 years, so remaining time (T₃) = 10 − (3 + 5) = 2 years

Rate for the remaining 2 years (R₃) = 9% per annum

Total Simple Interest (SI) paid at the end = ₹6800

Formula Used:

Simple Interest (SI) = (P × R × T) ÷ 100

Calculations:

⇒ Total SI = SI₁ + SI₂ + SI₃

⇒ 6800 = (P × 5 × 3) ÷ 100 + (P × 7 × 5) ÷ 100 + (P × 9 × 2) ÷ 100

⇒ 6800 = (15P ÷ 100) + (35P ÷ 100) + (18P ÷ 100)

⇒ 6800 = (15P + 35P + 18P) ÷ 100

⇒ 6800 = 68P ÷ 100

⇒ P = (6800 × 100) ÷ 68

⇒ P = 10000

∴ The correct answer is ₹10000.

Additional Information

Effective Rate of Simple Interest

When money is borrowed at different rates for different periods, the total effective percentage interest is simply the sum of the products of each rate and its respective time period: R_effective = R₁T₁ + R₂T₂ + ...

Amount in Simple Interest

The total amount to be repaid at the end of the term is the sum of the Principal and the Simple Interest generated: A = P + SI = P(1 + RT ÷ 100).

Difference Between SI and CI

Unlike Compound Interest where interest is calculated on the accumulated interest at the end of each cycle, Simple Interest is always calculated solely on the initial Principal amount for the entire duration.

Shortcut Trick Base area of a cone = πr2 Lateral surface area = πrl Equating both as per the given condition: πr2 = πrl Canceling π and r from both sides directly gives: l = r ∴ The correct answer is r.

Alternate Method

r l h

Given: Radius of the cone = r Slant height of the cone = l Area of the base = Lateral surface area Formula Used: Area of base of a cone = πr2 Lateral surface area of a cone = πrl Calculations: ⇒ According to the question, Area of base = Lateral surface area ⇒ πr2 = πrl ⇒ Dividing both sides by πr (since r > 0) ⇒ r = l ∴ The correct answer is r.

Additional Information Total Surface Area of a Cone The total surface area includes the area of the circular base and the curved lateral surface: TSA = πr(l + r). Volume of a Cone The volume represents the 3D space enclosed by the cone: V = (1÷3)πr2h, where h is the perpendicular height. Slant Height Relationship The slant height (l), base radius (r), and perpendicular height (h) form a right-angled triangle. Applying Pythagoras theorem: l = √(r2 + h2).

Shortcut Trick

Area of remaining field = Area of Square − Area of Pond

Area of remaining field = (Side)² − 616

Area of remaining field = 28² − 616

Area of remaining field = 784 − 616 = 168 m²

∴ The correct answer is 168 m².

Alternate Method

Pond Area = 616 m2

28 m

28 m Field Field

Given:

Side of the square field (a) = 28 m

Area of the circular pond = 616 m²

Formula Used:

Area of a square = a²

Area of remaining part = Area of square − Area of internal shape

Calculations:

⇒ Area of the square field = 28 × 28

⇒ Area of the square field = 784 m²

⇒ Area of the remaining field = Area of square field − Area of pond

⇒ Area of the remaining field = 784 − 616 = 168 m²

∴ The correct answer is 168 m².

Additional Information

Square Properties

Area = a² | Perimeter = 4a | Diagonal = a√2

Circle Properties

Area = πr² | Circumference = 2πr (where r is the radius)

Largest Circle in a Square

When a circle perfectly fits inside a square of side a, its radius is a/2. It occupies exactly π/4 (approx. 78.5%) of the square's total area.

Shortcut Trick

Volume of any right prism = Base Area × Height.

Since the base area remains constant, Volume ∝ Height.

Therefore, the percentage change in volume will be exactly equal to the percentage change in height.

Given percentage increase in height = 50%.

⇒ Percentage increase in volume = 50%.

∴ The correct answer is 50%.

Alternate Method

Given:

Increase in height of the right prism = 50%

Base area remains constant.

Formula Used:

Volume of a Right Prism = Base Area × Height

h V = Ah Area = A

1.5h V' = 1.5Ah Area = A

+50% Height

Calculations:

⇒ Let the initial height of the prism = h

⇒ Let the constant base area of the prism = A

⇒ Initial Volume (V₁) = A × h = Ah

⇒ New height of the prism = h + (50 ÷ 100) × h = 1.5h

⇒ New Volume (V₂) = A × 1.5h = 1.5Ah

⇒ Increase in Volume = V₂ − V₁ = 1.5Ah − Ah = 0.5Ah

⇒ Percentage Increase in Volume = (Increase in Volume ÷ Initial Volume) × 100

⇒ Percentage Increase = (0.5Ah ÷ Ah) × 100 = 50%

∴ The correct answer is 50%.

Additional Information

Volume of a Prism

Volume = Base Area × Height. If the base area is kept constant, the volume is directly proportional to the height.

Volume of a Pyramid or Cone

Volume = 1/3 × Base Area × Height. It is exactly one-third the volume of a right prism having the same base area and height.

Successive Percentage Change

If the height changes by a% and the base area changes by b%, the overall percentage change in volume can be evaluated using the successive formula: a + b + (a × b)/100.

Shortcut Trick

The percentage area of a minor segment formed by an equilateral triangle at the center is independent of the circle's radius.

Required % = [(Area of Sector − Area of Triangle) ÷ Total Area] × 100

Required % = (1 ÷ 6 − √3 ÷ 4π) × 100 = (0.1667 − 1.732 ÷ 12.56) × 100

Required % = (0.1667 − 0.1379) × 100 = 0.0288 × 100 = 2.88%

∴ The correct answer is 2.88%.

Alternate Method

Given:

Radius of the clock (r) = 20 cm

Central angle (θ) = 60° (since the chord and two radii form an equilateral triangle)

π = 3.14, √3 = 1.732

Formula Used:

Total Area of Clock = πr²

Area of Sector = (θ ÷ 360) × πr²

Area of Equilateral Triangle = (√3 ÷ 4) × r²

O

60° r = 20 r = 20 Chord A B

Painted Minor Segment

Calculations:

⇒ Total Area = 3.14 × 20² = 3.14 × 400 = 1256 cm²

⇒ Area of Sector = (60 ÷ 360) × 1256 = 1256 ÷ 6 ≈ 209.33 cm²

⇒ Area of Triangle = (1.732 ÷ 4) × 400 = 1.732 × 100 = 173.20 cm²

⇒ Area of Painted Segment = Area of Sector − Area of Triangle

⇒ Area of Painted Segment = 209.33 − 173.20 = 36.13 cm²

⇒ Required Percentage = (36.13 ÷ 1256) × 100 = 2.876% ≈ 2.88%

∴ The correct answer is 2.88%.

Additional Information

Area of a Sector

The area of a sector of a circle with radius r and central angle θ in degrees is given by the formula (θ ÷ 360) × πr².

Area of a Circular Segment

A segment is the region bounded by a chord and an arc. The area of a minor segment is calculated as the Area of the corresponding Sector − Area of the Triangle formed by the two radii and the chord.

Equilateral Triangle Area

An equilateral triangle has all sides equal and internal angles of exactly 60°. Its total area can be determined using the direct formula (√3 ÷ 4) × side².

Shortcut Trick

Since the hole is bored through the entire height, the ratio of the volume removed depends only on the square of the radii.

Volume Removed % = (r_hole ÷ R_original)² × 100

⇒ Volume Removed % = (2 ÷ 4)² × 100

⇒ (1/2)² × 100 = 25%

∴ The correct answer is 25%.

Alternate Method

Given:

Radius of original cylinder (R) = 4 cm

Height of original cylinder (h) = 10 cm

Radius of bored hole (r) = 2 cm

Height of bored hole = 10 cm (full height)

R = 4 cm r = 2 cm

h = 10 cm

Volume Removed = Inner Hole Volume

Formula Used:

Volume of cylinder = πr²h

Percentage removed = (Volume removed ÷ Original volume) × 100

Calculations:

⇒ Original volume = π × (4)² × 10

⇒ Original volume = 160π cm³

⇒ Volume removed (Hole) = π × (2)² × 10

⇒ Volume removed = 40π cm³

⇒ Percentage removed = (40π ÷ 160π) × 100

⇒ Percentage removed = (1 ÷ 4) × 100 = 25%

∴ The correct answer is 25%.

Additional Information

Volume of a Hollow Cylinder

The volume of the material remaining after boring a hole is determined by calculating the difference in volume: V = πh(R² − r²).

Curved Surface Area of a Hollow Cylinder

The total curved surface area becomes the sum of the inner hole's area and the outer cylinder's area: CSA = 2πRh + 2πrh = 2πh(R + r).

Total Surface Area of a Hollow Cylinder

The total surface area includes the inner and outer curved areas plus the area of the top and bottom solid rings: TSA = 2πh(R + r) + 2π(R² − r²).

Shortcut Trick

For sectors of the same circle, the area is directly proportional to the central angle.

Angle of the first sector = 45°

Angle of the second sector = π/4 radians = (180° ÷ 4) = 45°

Since both central angles are equal, their areas will be exactly the same.

∴ The correct answer is 1:1.

Alternate Method

Given:

Radius of the circle (r) = 15 cm

Central angle of first sector (θ₁) = 45°

Central angle of second sector (θ₂) = π/4 radians

45° r = 15 cm First Sector

π/4 r = 15 cm Second Sector

Ratio = ?

Formula Used:

Area of a sector (when θ is in degrees) = (θ ÷ 360°) × πr²

Area of a sector (when θ is in radians) = (1 ÷ 2) × r²θ

Calculations:

⇒ Area of first sector = (45° ÷ 360°) × π × (15)²

⇒ Area of first sector = (1 ÷ 8) × 225π = 28.125π cm²

⇒ Area of second sector = (1 ÷ 2) × (15)² × (π ÷ 4)

⇒ Area of second sector = (1 ÷ 2) × 225 × (π ÷ 4) = 28.125π cm²

⇒ Ratio of areas = Area of first sector : Area of second sector

⇒ Ratio = 28.125π : 28.125π = 1 : 1

∴ The correct answer is 1:1.

Additional Information

Area of a Sector

The area of a sector of a circle with radius r and central angle θ is given by (θ ÷ 360°) × πr² if θ is measured in degrees, and (1 ÷ 2)r²θ if θ is measured in radians.

Radian to Degree Conversion

To convert an angle from radians into degrees, multiply the radian value by (180° ÷ π). For example, π radians equals 180°.

Length of an Arc

The arc length of a corresponding sector is calculated as (θ ÷ 360°) × 2πr (for degrees) or simply rθ (for radians).

The correct answer is: Inexperienced.

Key Points

• The word "Callow" means someone who is young, immature, or lacking experience. (अनुभवहीन)
• Example: The callow intern struggled to adapt to the fast-paced environment of the corporate world.
• "Inexperienced" refers to someone who does not have much practice, knowledge, or exposure in a particular field or activity. (अनुभवहीन)
• Example: As an inexperienced driver, she was nervous about driving on the highway.
• Hence, the synonym of "Callow" is "Inexperienced".

Therefore, the correct answer is: Inexperienced.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Experienced (अनुभवी): Someone who has knowledge or skill gained through practice or exposure to a particular activity.
• Example: The experienced chef crafted a meal that amazed everyone at the table.
• Wise (बुद्धिमान): Someone who has good judgment, knowledge, or insight, often gained through experience.
• Example: The wise old man offered advice that changed the young boy's perspective.
• Mature (परिपक्व): Someone who is fully developed or grown, both physically and mentally.
• Example: She handled the situation in a mature manner, showing great composure.

The correct answer is: Option 3) Aggravating.

Key Points

• The word "Placatory" means intended to make someone less angry or hostile; soothing or pacifying. (शांत करने वाला)
• Example: She spoke in a placatory tone to calm the agitated crowd.
• "Aggravating" refers to something that makes a situation worse or more serious, or causes annoyance or anger. (उत्तेजित करने वाला)
• Example: His constant interruptions during the meeting were highly aggravating to everyone present.
• Hence, the opposite of 'Placatory' is 'Aggravating'.

Therefore, the correct answer is: Option 3) Aggravating.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Pacifying (शांत करना): To calm or soothe someone who is angry or upset.
• Example: The mother’s pacifying words helped her child stop crying.
• Soothing (सुकून देने वाला): Having a calming or comforting effect.
• Example: The sound of the ocean waves was very soothing.
• Conciliatory (समझौतापूर्ण): Intended to placate or pacify; aimed at ending disagreement or hostility.
• Example: The CEO adopted a conciliatory approach to resolve the labor dispute.

The correct answer is: Option 1.

Key Points

• The idiom "Blow hot and cold" means to change one's mood, opinion, or attitude frequently, often causing confusion or inconsistency. (बार-बार अपना मत या व्यवहार बदलना)
• Example: She always blows hot and cold about her plans, so we never know where she stands.
• Hence, the correct meaning of the idiom is "To change one's mood or opinion frequently." (बार-बार अपना विचार या मन बदलना)
• Example: His tendency to blow hot and cold makes it difficult to work with him effectively.

Therefore, the correct answer is: Option 1.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Option 2: To talk boastfully (गर्वपूर्ण ढंग से बात करना): Refers to speaking in an exaggerated manner about oneself or one's achievements.
• Example: He talked boastfully about how he single-handedly completed the project.
• Option 3: To enjoy both success and failure (सफलता और असफलता दोनों का आनंद लेना): Suggests experiencing both good and bad outcomes in life.
• Example: Life teaches us to enjoy both success and failure as part of the journey.
• Option 4: To remain consistent in behavior (व्यवहार में स्थिर रहना): Refers to maintaining the same attitude or approach without wavering.
• Example: Despite the challenges, she remained consistent in her behavior.

The correct answer is: Sincere.

Key Points

• The word "Fulsome" means excessive or insincere praise that might come across as overdone or exaggerated. (अत्यधिक या दिखावटी प्रशंसा)
• Example: His fulsome compliments made everyone doubt his sincerity.
• "Sincere" refers to being genuine, honest, and free from pretense or deceit. (ईमानदार और सच्चा)
• Example: Her sincere apology was appreciated by everyone.
• Hence, we can infer that the opposite of 'Fulsome' is 'Sincere'.

Therefore, the correct answer is: Sincere.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Overdone (अत्यधिक किया हुआ): Something that is excessive or exaggerated beyond what is necessary.
• Example: The decorations at the party were overdone and too flashy.
• Excessive (अत्यधिक): More than necessary, too much.
• Example: His excessive demands made it hard to work with him.
• Lavish (शानदार): Rich, elaborate, or luxurious.
• Example: They threw a lavish party to celebrate their anniversary.

The correct answer is option 3.

Key Points

The correct spelling is 'Proprioception'.

• Proprioception refers to the ability to sense the position, movement, and action of body parts. It is sometimes referred to as the "sixth sense."
• This sensory ability helps humans maintain balance and coordinate movements efficiently.
• For Example -
• Thanks to proprioception, you can touch your nose with your finger even with your eyes closed.

Therefore, the correct answer is 'Proprioception'.

Additional Information

Let's understand the incorrect options:

• Propriozeption - Incorrect spelling.
• Propiocaption - Incorrect spelling.
• Proprioseption - Incorrect spelling.

The correct answer is: Option 3 i.e. Paradox.

Key Points

• The word "Paradox" means a statement that appears self-contradictory or absurd but may hold a hidden truth. (विरोधाभास)
• Example: "Less is more" is a popular paradox that emphasizes how simplicity can lead to greater impact.
• Explanation of the Correct Word: A paradox is often used to provoke thought or reveal deeper insights into a concept. (विरोधाभास)
• Example: The paradox of time is that while it is infinite, our time on Earth is finite.

Therefore, the correct answer is: Option 3 i.e. Paradox.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Axiom (स्वयंसिद्ध): A self-evident truth that requires no proof.
• Example: In mathematics, the statement "The whole is greater than the part" is an axiom.
• Maxim (सूक्ति): A short, pithy statement expressing a general truth or rule of conduct.
• Example: "Actions speak louder than words" is a well-known maxim.
• Irony (विडंबना): The expression of one's meaning by using language that normally signifies the opposite, typically for humorous or emphatic effect.
• Example: It was ironic that the fire station burned down.

The correct answer is 'when'.

Key Points

• The phrase "Scarcely had..." is a common structure in English, and it is followed by the conjunction "when."
• The use of "when" indicates that one action occurred immediately after another.
• Option 1: "than" is incorrect because it is typically used in comparisons.
• Option 3: "before" is incorrect as it does not suit the context of the sentence.
• Option 4: "until" is incorrect as it implies a different meaning related to the timing of an event.

Therefore, the correct answer is Option 2.

Complete Sentence: "Scarcely had the satellite deployed when it transmitted its first data packet."

Additional Information

• Option 1: "than" is incorrect as it does not align with the grammatical structure of the sentence.
• Option 3: "before" implies a prior action, which is not the intended meaning here.
• Option 4: "until" suggests a delay in action, which is not relevant in this context.

The correct answer is 'Upon'.

Key Points

• The word "Upon" is commonly used to indicate an action or event happening immediately after something else.
• In this sentence, "Upon" correctly connects the completion of the feasibility study with the team's request for additional funding.
• Option 1: "Having" is grammatically incorrect as it does not fit the sentence structure properly.
• Option 2: "On" is incorrect because it does not convey the sense of immediate sequence in this context.
• Option 4: "Despite" is incorrect because it implies contrast, which does not align with the intended meaning of the sentence.

Therefore, the correct answer is Option 3.

Complete Sentence: "Upon having completed the feasibility study, the team requested additional funding."

Additional Information

• Option 1: "Having" is a participial phrase, but in this case, it does not correctly fit the syntax or meaning of the sentence.
• Option 2: "On" is not the best choice as it does not express the immediate sequence of actions as effectively as "Upon" does.
• Option 4: "Despite" introduces a sense of contrast or contradiction, which is not relevant to the context of the sentence.

The correct answer is 'be'.

Key Points

• The verb "be" is used in the subjunctive mood to indicate necessity, urgency, or importance.
• In this context, the sentence expresses an imperative action that must be completed before the close of business.
• Options 1, 2, and 4 are incorrect because they do not fit the grammatical structure or intended meaning of the sentence.

Therefore, the correct answer is Option 3.

Complete Sentence: "It was imperative that the document be signed before the close of business."

Additional Information

• Option 1: "will be" is incorrect because it changes the tense to future, which does not fit the imperative nature of the sentence.
• Option 2: "was" is incorrect because it suggests the action has already been completed, contradicting the urgent requirement.
• Option 4: "had been" is incorrect because it refers to a past perfect tense that does not align with the sentence structure or meaning.

The correct answer is Option 2.

Key Points

• The error lies in part 2 of the sentence: "rather than compulsory have led."
• The subject "The perception" is singular, so the verb should be singular as well.
• The correct phrase should be "has led" instead of "have led."
• Thus, the error is in part 2 of the sentence.

Therefore, the correct answer is Option 2.

Correct Sentence: "The perception that the guidelines are optional rather than compulsory has led to widespread inconsistencies in compliance across state-level implementations."

Additional Information

• Part 1: "The perception that the guidelines are optional" – This part of the sentence is correct and does not require any changes.
• Part 3: "to widespread inconsistencies in compliance" – This part of the sentence is grammatically correct and does not require any changes.
• Part 4: "across state-level implementations" – This part of the sentence is grammatically correct and does not require any changes.

The correct answer is Option 1.

Key Points

• Passive voice structure: The object of the active voice sentence becomes the subject of the passive voice sentence.
• In the active voice, the sentence is: "Historians may well reinterpret the artifact after new evidence emerges."
• To convert to passive voice: Place the object "the artifact" at the beginning.
• Change the active verb form "may well reinterpret" to "may well be reinterpreted" (modal verb passive structure).
• Add the preposition "by" followed by the original subject "historians."
• Ensure the phrase "after new evidence emerges" remains at the end of the sentence for clarity.

Therefore, the correct answer is Option 1.

Correct Sentence: "The artifact may well be reinterpreted by historians after new evidence emerges."

Additional Information

• Option 2: "The artifact may have been reinterpreted by historians after new evidence emerges." – Incorrect tense (past perfect passive).
• Option 3: "The artifact will be reinterpreted well by historians after new evidence emerges." – Incorrect adverb placement and verb structure.
• Option 4: "The artifact could well be reinterpreting by historians after new evidence emerges." – Incorrect verb form.