SSC CGL 2025 (Held On: 13 Sept, 2025 Shift 3) (Previous Year Paper)

The logic followed here is:

Hence, the correct answer is "Option 4".

The logic followed here is:

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

Hence, the correct answer is "Option 3".

The logic followed here is:

Pattern: Each term = (previous term × previous term) − (previous term − 1)

Check the sequence:

1 → 2 → 1×1 +1 = 2 

2 → 5 → 2×2 +1 = 5 

5 → 26 → 5×5 +1 = 26 

Similarly,

next term = 26 × 26 + 1 = 676 + 1 = 677

Hence, the correct answer is "Option 1".

The logic followed here is:

Check the numbers: 29, 31, 47, 101

All numbers are prime numbers (divisible only by 1 and themselves).

Check the options:

Option 1) 111 → Not prime (divisible by 3, 37) 

Option 2) 103 → Prime 

Option 3) 147 → Not prime (divisible by 3, 7, 7) 

Option 4) 196 → Not prime (divisible by 2, 98) 

So, the number similar to the given sequence is 103.

Hence, the correct answer is "Option 2".

Given:

Statement:

The government has decided to implement stricter regulations on industrial pollution to curb the growing environmental concerns.

Assumptions:

I. Industrial pollution is a significant cause of environmental degradation – True (The decision to regulate industrial pollution assumes it significantly affects the environment).

II. Stricter regulations will reduce industrial pollution – True (Implementing stricter regulations assumes they will have the intended effect).

III. Environmental concerns are primarily related to industrial activities – False (The statement does not assume that all environmental concerns are only due to industrial activities; other sources may exist).

So, Only assumptions I and II are implicit.

Hence, the correct answer is "Option 1".

Given word: COMFORT

Arrange letters in alphabetical order:

C, F, M, O, O, R, T

Check each letter’s position in the original word vs alphabetical order:

Original: C O M F O R T

Alphabetical: C F M O O R T

Positions unchanged: C (1), M (3), O (5), R (6), T (7) → 5 letters

Hence, the correct answer is "Option 4".

The address given in the problem is,

Flat No. 12B, Building 7, Sector 15, Sohna Road, Gurgaon, Haryana - 122001

Now, match this address with the given options:

So, address Option 4 is exactly identical to the given address.

Hence, the correct answer is option 4.

Given word: SCHOOL

First, second, third, and fifth letters of SCHOOL → S, C, H, O

We need to form meaningful four-letter words using S, C, H, O (each letter used once).

Check possible meaningful words:

COSH → Yes, a word

HOSC → No

SCHO → No

CHOS → No

OCHS → No

HOCS → No

Only COSH is meaningful.

Hence, the correct answer is "Option 1".

Given:

Amit is 12th from the left.

Sunil is 15th from the right.

After they interchange their positions, Amit becomes 17th from the left.

That means Sunil’s original position from the left was 17.

Now, If a person is 17th from the left and 15th from the right, then

Total persons = 17 + 15 − 1

= 32 − 1

= 31

So, total number of persons in the row is 31.

Hence, the correct answer is "Option 3".

The logic followed here is:

CUT : BDTVSU

Similarly,

TIP : ?

Hence, the correct answer is "Option 2".

The logic followed here is:

WRITE : JEVGR

Similarly,

WRONG : ?

Hence, the correct answer is "Option 1".

The logic followed here is:

Check the series: 1, 4, ___, 16, 25

These are perfect squares:

1 = 1²

4 = 2²

? = 3² = 9

16 = 4²

25 = 5²

So, the missing number is 9.

Hence, the correct answer is "Option 3".

The logic followed here is:

Check the pattern in each group:

Option 1: M1$ : N2# : O3@

Letters: M → N → O (consecutive) 

Numbers: 1 → 2 → 3 (consecutive) 

Symbols: $, #, @ (pattern changes, but consistent as sequence of symbols) 

Option 2: P4% : Q5^ : R6&

Letters: P → Q → R (consecutive) 

Numbers: 4 → 5 → 6 (consecutive) 

Symbols: %, ^, & (pattern consistent) 

Option 3: S7 : T8( : U9)*

Letters: S → T → U (consecutive) 

Numbers: 7 → 8 → 9 (consecutive) 

Symbols: *, (, ) (pattern consistent) 

Option 4: V10_ : X11@ : Y13#

Letters: V → X → Y (not consecutive; skips W) 

Numbers: 10 → 11 → 13 (not consecutive; skips 12) 

Symbols: _, @, # (pattern okay)

So, Option 4 breaks the letter and number sequence pattern.

Hence, the correct answer is "Option 4".

Given: A hexagon has 6 sides.

Number of diagonals =  n × (n − 3) ÷ 2

= 6 × (6 − 3) ÷ 2

= 6 × 3 ÷ 2

= 18 ÷ 2

= 9

Hence, the correct answer is Option 1.

The logic followed here is:

Pattern: A @ B = A² + B

Check:

5 @ 1 = 25 + 1 = 26 

3 @ 4 = 9 + 4 = 13 

Similarly, 6 @ 2 = 36 + 2 = 38

Hence, the correct answer is "Option 2".

The logic followed here is:

Given: PHANTOM → KLSQZLN

Applying this same pattern to SPECTOR:

Therefore, SPECTOR is coded as HTWFZLI.

Hence, the correct answer is "Option 3".

The logic followed here is:

Logic: Each letter in the word is shifted +1 in the alphabet, except the 4th letter, which is shifted by -1.

PEARL → QFBQM

​

Similarly, STONE →

So, STONE is coded as TUPMF.

Hence, the correct answer is "Option 2".

Given: a 40 L solution with salt and water in 3:5 ratio, the amount of salt is 15 L and water is 25 L.

Let x liters of water be added to make the ratio 3:7.

15 divided by (25 + x) = 3 divided by 7

105 = 3 × (25 + x)

105 = 75 + 3x

3x = 30

x = 10

So, 10 L of water should be added.

Hence, the correct answer is Option 1.

The logic followed here is:

Pattern: The value of “A & B” = A² + B²

Now,

1. 3 & 4

= 3² + 4²

= 9 + 16

= 25

2. 5 & 2

= 52 + 22

= 25 + 4

= 29

3) 6 & 3

= 62 + 32

= 36 + 9

= 45

Hence, the correct answer is "Option 3".

Family Chart:

Given: 

Statement: "He is the only son of my mother's only son."

"My mother's only son" → Sohan himself (assuming Sohan is the only son).

"The only son of my mother's only son" → Sohan’s son.

So, the man is Sohan’s son.

Hence, the correct answer is "Option 2".

Family Chart:

Given: 

P's brother is Q.

Q is the father of R.

R is the sister of S. 

As S's gender is not known yet. So, S's relation to P cannot be determined.

Hence, the correct answer is "Option 4".

The logic followed here is:

After interchanging + & × and 6 & 10, check each option.

Interchange rules: + becomes ×, × becomes +,6 becomes 10,10 becomes 6

Option 1: (6+3)×10 = 36

After interchanging: (10 × 3) + 6 = 36

⇒ 30 + 6 = 36

⇒ 36 = 36

Option 2: (10+2)×6 = 20

After interchanging: (6 × 2) + 10 = 20

⇒ 12 + 10 = 22

⇒ 22 ≠ 20

Option 3: (6+5)×10 = 50

After interchanging: (10 × 5) + 6 = 50

⇒ 50 + 6 = 56

⇒ 56 ≠ 50

Option 4: (10+4)×6 = 30

After interchanging: (6 × 4) + 10 = 30

⇒ 24 + 10 = 34

⇒ 34 ≠ 30

Hence, the correct answer is "Option 1".

BODMAS Table: 

Given expression: 20 M 4 L 3 J 5 = ?

Now, ‘J’ means ‘+’, ‘K’ means ‘−’, ‘L’ means ‘×’ and ‘M’ means ‘÷’

So, the expression becomes: 20 ÷ 4 × 3 + 5

Now apply BODMAS:

⇒ 20 ÷ 4 × 3 + 5

⇒ 5 × 3 + 5

⇒ 15 + 5

⇒ 20

Hence, the correct answer is "Option 1".

BODMAS Table: 

Given equation: 12 + 4 × 2 - 3 = ?

Now, If + = ÷, - = x, x = +,  Then the expression becomes:

⇒ 12 ÷ 4 + 2 × 3 = ?

Now apply BODMAS:

⇒ 12 ÷ 4 + 2 × 3

⇒ 3 + 2 × 3

⇒ 3 + 6

⇒ 9

Hence, the correct answer is "Option 2".

Given numbers: 41 and 36

Sum of 41 and 36 = 41 + 36 = 77

Multiply the sum by 9 → 77 × 9

Calculation:

77 × 9 = (70 × 9) + (7 × 9) = 630 + 63 = 693

Hence, the correct answer is "Option 2".

The correct answer is Lauriya Nandangarh - Bihar.

Key Points

• Lauriya Nandangarh in Bihar is home to one of the Ashokan pillars, which is inscribed with edicts of Emperor Ashoka.
• The pillar at Lauriya Nandangarh is made of polished sandstone and has inscriptions that reflect the policies of Dhamma, promoting ethical governance and compassion.
• The site is significant as it represents Ashoka’s efforts to spread Buddhist principles and moral values across his empire.
• The Lauriya Nandangarh pillar is an example of Ashoka's architectural contributions, showcasing advanced craftsmanship and his commitment to disseminating his edicts.
• It is located in the West Champaran district of Bihar and is a major archaeological site of historical importance.

Additional Information

• Sarnath - Gujarat
• This pairing is incorrect as Sarnath is located in Uttar Pradesh, not Gujarat.
• Sarnath is the site where Gautama Buddha delivered his first sermon after attaining enlightenment, known as the Dharmachakra Pravartan.
• The Ashokan pillar at Sarnath is famous for its lion capital, which has been adopted as the National Emblem of India.
• The inscriptions on the pillar highlight Ashoka's vision of Dhamma and his call for ethical conduct and non-violence.
• Sanchi - Odisha
• The pairing is incorrect as Sanchi is located in Madhya Pradesh, not Odisha.
• Sanchi is known for its stupas and is a UNESCO World Heritage Site representing the rich Buddhist heritage of India.
• Although there are inscriptions and architectural elements associated with Ashoka, there is no Ashokan pillar at Sanchi.
• The site is historically significant for its connection to Ashoka’s promotion of Buddhism.
• Amaravati - Madhya Pradesh
• This pairing is incorrect as Amaravati is located in Andhra Pradesh, not Madhya Pradesh.
• Amaravati is known for its ancient Buddhist stupa and sculptures, but it does not host an Ashokan pillar.
• The site represents a key center of Buddhist art and culture during ancient times.

The correct answer is Collectiveness.

Key Points

• The Nyokum festival is celebrated by the Nyishi tribe of Arunachal Pradesh, India, to promote communal harmony and togetherness.
• The word "Kum" in Nyokum symbolizes collectiveness, reflecting the festival's emphasis on unity and community gathering.
• This festival involves rituals and prayers for prosperity, happiness, and the well-being of all living beings.
• Nyokum is typically celebrated in February, marking a blend of traditional culture, spirituality, and agricultural significance.
• It highlights the Nyishi people's bond with nature, as they pray to the deities and nature spirits for blessings and abundance in their lives.

Additional Information

• Major Festivals by Tribe/Region:
• Monpa:
• Losar: Tibetan New Year celebrated with purification, rituals, and apricot blossom festivals in Tawang/West Kameng.
• Torgya: A powerful Buddhist festival at Tawang Monastery with sacred mask dances (Sha-na Cham).
• Apatani:
• Dree: A major agricultural festival for bumper crops and prosperity, held in July.
• Myoko: A long festival reinforcing fertility and community bonds.
• Adi (Minyong/Padam):
• Solung: A colourful seven-day harvest festival with rice beer, feasts, and traditional dances.
• Idu Mishmi:
• Reh: A festival for prosperity, featuring shamanistic chants and invocations.

The correct answer is Shadav.

Key Points

• A raga that contains six notes is classified under the Shadav jaati.
• In Shadav ragas, the scale consists of six notes, which can be in the ascending (Arohana), descending (Avarohana), or both sequences.
• The Shadav classification is part of the Indian classical music system, which organizes ragas based on the number of notes used.
• Shadav ragas are known for their unique melodic expressions and are often used to evoke specific emotions and moods.
• Examples of Shadav ragas include Malkauns, Durga, and Bhupali.

Additional Information

• Audav:
• An Audav raga contains five notes in its scale.
• It is also referred to as a pentatonic scale in Indian classical music.
• Both the Arohana (ascending scale) and Avarohana (descending scale) in an Audav raga consist of five swaras (notes).
• Examples of Audav ragas include Bhupali and Mohanam.
• Sampoorna:
• A Sampoorna raga contains all seven notes (sapta swaras) in both the ascending (Arohana) and descending (Avarohana) scales.
• The word "Sampoorna" means complete, referring to the completeness of the scale.
• Sampoorna ragas are considered versatile and are widely used in Indian classical music.
• An example of a Sampoorna raga is Bilahari.
• Tishra:
• The term "Tishra" is used in the context of rhythm (tala) in Indian classical music rather than in the classification of ragas.
• It refers to a rhythmic cycle with three beats or a subdivision of three counts in a tala.
• Tishra is often utilized in compositions to create unique rhythmic patterns.

The correct answer is Hitting the ball twice deliberately results in dismissal..

Key Points

• Hitting the ball twice deliberately is considered an illegal action in cricket and results in dismissal under the laws of the game.
• This dismissal is covered under Law 34 of the MCC Laws of Cricket, which prohibits a batter from intentionally striking the ball twice unless it is done to defend their wicket.
• Such an action is judged by the umpire, who determines whether the batter deliberately hit the ball twice.
• The first strike is considered legitimate (e.g., hitting the ball with the bat), but the second strike intended to gain runs or mislead the fielding team constitutes a breach.
• This rule upholds the integrity of fair play in cricket and ensures that the batter does not use unfair methods to gain an advantage.

Additional Information

• Retired Out:
• A player retiring out does not need umpire approval; it is the batter's voluntary decision.
• Unlike "retired hurt," where a player leaves due to injury with an option to return, "retired out" is final and does not allow re-entry into the game.
• This form of dismissal is uncommon and usually occurs in practice matches or under special circumstances.
• Obstructing the Field:
• According to Law 37 of the MCC Laws of Cricket, "Obstructing the Field" occurs when a batter deliberately interferes with a fielder attempting to field or catch the ball.
• This dismissal is not accidental; it requires clear intent by the batter to obstruct the fielding side.
• Examples include using the bat or body to stop the ball while a fielder is attempting to effect a run-out or catch.
• Accidental interference, such as running in the path of a fielder without intent, does not constitute this dismissal.
• Cricket Dismissals:
• There are several ways a batter can be dismissed in cricket, including bowled, caught, leg before wicket (LBW), stumped, and run-out.
• Other less common dismissals include obstructing the field, retired out, hitting the ball twice, and timed out.
• Each type of dismissal has specific rules outlined by the MCC Laws of Cricket and is subject to umpire judgment.

The correct answer is Roop Singh.

Key Points

• Roop Singh was an Indian field hockey player who played a crucial role in India’s historic Olympic victories in the 1930s.
• In the 1932 Summer Olympics held in Los Angeles, India defeated the USA with a record-breaking score of 24-1 in hockey.
• Roop Singh scored an incredible 10 goals in this match, showcasing his exceptional skill and earning a place in hockey history.
• He was the younger brother of Dhyan Chand, often referred to as the “Wizard of Hockey,” and together they formed a legendary duo in Indian hockey.
• Roop Singh’s contribution to the game is celebrated as one of the finest performances in Olympic hockey history.

Additional Information

• Dhyan Chand:
• Dhyan Chand, often referred to as the “Wizard of Hockey,” is widely regarded as one of the greatest hockey players of all time.
• He represented India in the Olympics three times (1928, 1932, and 1936) and was instrumental in securing gold medals for the country in all these events.
• Dhyan Chand scored multiple goals across these tournaments, earning global fame for his extraordinary dribbling skills and precision.
• He received the Padma Bhushan, India’s third-highest civilian award, in 1956 for his contribution to sports.
• Balbir Singh Sr.:
• Balbir Singh Sr. was another legendary hockey player who represented India in the Olympics in later years (1948, 1952, and 1956).
• He played a key role in securing three consecutive Olympic gold medals for India.
• Balbir Singh Sr. is remembered for scoring five goals in the 1952 Olympic final against the Netherlands, setting a record for the highest number of goals in an Olympic final match.
• He was awarded the Padma Shri in recognition of his contributions to Indian hockey.
• Leslie Claudius:
• Leslie Claudius was an Indian hockey player who won three Olympic gold medals (1948, 1952, and 1956) and one silver medal (1960) during his illustrious career.
• He was known for his defensive skills and played a key role as a half-back in the Indian hockey team.
• Leslie Claudius holds the distinction of being one of the most decorated Olympians in hockey.
• He was awarded the Padma Shri for his contributions to the sport of hockey.

The correct answer is BRICS Startup Forum.

Key Points

• The BRICS Startup Forum was launched in 2021 under India's BRICS Presidency to foster collaboration among startups from BRICS nations.
• This initiative aims to promote cross-border innovation, knowledge sharing, and funding access for startups within the BRICS economies (Brazil, Russia, India, China, and South Africa).
• The forum serves as a platform for startups, investors, and ecosystem enablers to network and explore partnerships across diverse sectors.
• The BRICS Startup Forum aligns with India's vision of fostering entrepreneurship and innovation as a means to drive economic growth and development.
• The initiative complements existing BRICS mechanisms, such as the New Development Bank, to enhance economic cooperation and sustainable development.

Additional Information

• BRICS Innovation Pact:
• Although no formal initiative called the "BRICS Innovation Pact" exists, innovation is a core theme under BRICS cooperation.
• BRICS nations have collaborated on several innovation-related initiatives, including technology transfer, R&D partnerships, and skill development programs.
• BRICS SME Exchange:
• This refers to a conceptual framework aimed at improving cooperation between small and medium enterprises (SMEs) across BRICS countries.
• The objective is to provide SMEs with opportunities for market access, funding, and knowledge sharing.
• BRICS Economic Dialogue:
• The BRICS Economic Dialogue is a platform that facilitates discussions on economic policies, trade, and investment opportunities among BRICS nations.
• It aims to strengthen economic ties and address global economic challenges through collective action.

The correct answer is Option 1 (Only 1 is correct).

Key Points

• The book The Neeraj Chopra Story: The Man Who Made History focuses on detailing the journey of Neeraj Chopra, India’s first-ever Olympic gold medalist in athletics.
• It highlights Neeraj's training, mindset, and the challenges he faced while making his historic achievements in javelin throwing.
• The book also describes Neeraj’s discipline, perseverance, and the hard work that went into achieving his Olympic feat.
• This biography serves as an inspiration for young athletes and aspiring sportspeople in India and across the globe.
• The book was not written by his former Olympian coach; this information is inaccurate.

Additional Information

• Golden Throw: The Neeraj Chopra Story: An epic tale of resilience and dedication, aimed at young readers and sports fans.
• Neeraj Chopra: A Complete Biography: Explores his journey from a small town to Olympic gold, intended to motivate youth.
• Neeraj Chopra: India's Golden Javelin: Another biography focusing on his Olympic success.
• Neeraj Chopra: Attitude is Everything by Ankit Chauhan: An e-book exploring his mindset and journey.

The correct answer is Floodplains of large rivers.

Key Points

• Natural levees are elevated ridges formed along the banks of large rivers due to the deposition of sediments during flooding events.
• They are most commonly associated with floodplains of large rivers, where rivers periodically overflow and deposit heavier sediments close to their banks.
• The formation of natural levees helps reduce subsequent flooding as they act as natural barriers to river overflow.
• Such levees are prominent features in lowland river systems such as the Mississippi River in the USA and the Ganges River in India.
• Natural levees play a crucial role in shaping the landscape and agricultural practices in floodplain regions, as they create a distinct elevated area suitable for cultivation and settlement.

Additional Information

• Arid Deserts
• Arid deserts are characterized by low precipitation, extreme temperatures, and sparse vegetation.
• These regions are dominated by aeolian (wind-driven) processes, such as the formation of sand dunes and erosion, rather than fluvial processes.
• Natural levees are not typically found in arid deserts due to the lack of consistent water flow and sediment deposition.
• Glacial Valleys
• Glacial valleys are U-shaped valleys carved by the movement of glaciers over time.
• These areas are dominated by glacial processes, including the deposition of moraines and other glacial sediments.
• Natural levees are not associated with glacial valleys, as they are formed by rivers, not glaciers.
• Coastal Lagoons
• Coastal lagoons are shallow water bodies separated from the ocean by a barrier, such as sandbars or barrier islands.
• They are influenced by tidal and wave action, rather than riverine processes, which are responsible for the formation of natural levees.
• These environments are more associated with marine and estuarine ecosystems.

The correct answer is The final was held in Bhubaneswar where India defeated Lebanon..

Key Points

• The 2023 Intercontinental Cup final was held in Bhubaneswar, Odisha.
• India defeated Lebanon 2-0 in the final, securing their third Intercontinental Cup title.
• The match was held at the Kalinga Stadium, which has become a prominent venue for hosting international sports events.
• Sunil Chhetri, India’s captain, played a crucial role throughout the tournament, demonstrating outstanding leadership and performance.
• This victory marked a significant achievement for the Indian football team under the guidance of coach Igor Stimac.

Additional Information

• Main Theme: 2023 Intercontinental Cup
• The Intercontinental Cup is a football tournament organized by the All India Football Federation (AIFF).
• The competition serves as preparation for India’s senior men’s national team ahead of major international tournaments.
• Teams from Asia, Africa, and other regions participate in the tournament.
• The 2023 edition saw India, Lebanon, Vanuatu, and Mongolia competing in the tournament.

The correct answer is Lavjibhai Parmar.

Key Points

• Lavjibhai Parmar is the first recognized artist in the traditional Tanglia weaving form of Gujarat.
• The Tanglia weaving technique involves creating intricate patterns using beads and threads, a craft unique to the Surendranagar district in Gujarat.
• He was honored with the prestigious Padma Shri in 2025 for his remarkable contribution to preserving and promoting this dying art form.
• Lavjibhai's innovative approach has brought Tanglia weaving to national and international attention, ensuring its survival and relevance in modern times.
• His work has been instrumental in empowering local artisans and preserving India’s rich cultural heritage.

Additional Information

• Shyam Bihari Agrawal
• An industrialist and philanthropist from Chhattisgarh, Shyam Bihari Agrawal has contributed significantly to social development through his charitable initiatives.
• He has been recognized for his efforts in education, healthcare, and rural development in central India.
• However, his work is unrelated to the Tanglia weaving tradition of Gujarat.
• Gokul Chandra Das
• Gokul Chandra Das is a prominent artist known for his mastery of traditional Assam silk weaving techniques, including Muga and Eri silk.
• His work highlights the unique textile heritage of Assam, which is different from Gujarat’s Tanglia weaving.
• Farooq Ahmad Mir
• Farooq Ahmad Mir is a noted craftsman from Jammu and Kashmir, specializing in Pashmina shawl weaving.
• His contributions have been pivotal in sustaining the traditional Pashmina craft of the region, which is distinct from Tanglia weaving.
• Tanglia Weaving
• Tanglia weaving is a traditional craft that integrates beadwork into handwoven textiles, creating beautiful geometric patterns.
• It is a labor-intensive process, requiring exceptional skill and precision.
• This art form primarily supports the livelihood of the Vankar community in Gujarat.
• Efforts by artisans like Lavjibhai Parmar have revived this craft, showcasing its potential in modern fashion and home decor markets.

The correct answer is 1, 2 and 3 all are correct.

Key Points

• Mushroom-shaped rocks, also known as pedestal rocks, are formed due to wind abrasion, where the lower portion erodes more quickly due to the concentration of sand particles near the ground. This creates a slender base and a broad cap.
• Flat-topped residual hills, resembling table surfaces, are called mesas. These are formed due to differential erosion in desert regions, leaving behind such flat-topped landforms.
• Rock remnants standing as isolated pedestals, or inselbergs, are created due to the erosional activities of wind, which remove the surrounding softer material, leaving harder rock remnants.
• Wind erosion is a predominant geomorphic process in desert regions and creates unique landforms such as yardangs, dunes, and deflation hollows.
• These features are characteristic of arid and semi-arid desert landscapes where wind plays a significant role in shaping the topography.

Additional Information

• Wind Erosion and Desert Landforms
• Wind erosion occurs primarily in arid regions due to the lack of vegetation cover and the abundance of loose, fine-grained particles that can be transported by wind.
• Common processes include deflation (removal of loose particles), abrasion (grinding of rock surfaces by windborne particles), and attrition (collision between particles).
• Desert landforms shaped by wind include dunes, yardangs, ventifacts, and blowouts.
• Pedestal Rocks or Mushroom-shaped Rocks
• These are formed due to differential erosion by wind, where the softer material at the base erodes faster than the harder upper layers.
• Such landforms are commonly found in arid zones and are indicative of wind abrasion near the surface.
• Mesas and Buttes
• Mesas are flat-topped hills with steep sides, formed due to erosion of sedimentary rock layers.
• Buttes are similar to mesas but smaller in size and are often remnants of larger mesas.
• Both are features of arid landscapes and result from the differential erosion of rock layers.
• Inselbergs
• Inselbergs are isolated rock outcrops that rise abruptly from the surrounding plains.
• They are formed due to the prolonged erosion of softer surrounding material, leaving behind hard rock masses.
• Examples include Uluru in Australia and Sugarloaf Mountain in Brazil.

The correct answer is 16th January 2025.

Key Points

• India successfully completed the SpaDeX (Space Docking Experiment) operation on 16th January 2025.
• The SpaDeX mission is a significant milestone in India’s space exploration capabilities, aimed at demonstrating autonomous docking technology in space.
• This operation was conducted by the Indian Space Research Organisation (ISRO), marking a major step forward in India’s ability to support in-orbit servicing and assembly of satellites.
• The successful completion of SpaDeX boosts India’s position in the global space industry and enhances the country’s self-reliance in advanced space technologies.
• The docking experiment is crucial for future missions, such as the Indian Human Spaceflight Programme (Gaganyaan), and for enabling space station development initiatives.

Additional Information

• Significance of SpaDeX:
• SpaDeX enables the demonstration of autonomous docking in orbit, a technology essential for long-term space exploration and maintenance of satellites.
• It lays the groundwork for future missions involving refueling, repair, and assembly of spacecraft in orbit.
• The mission is aligned with ISRO’s broader goals under the Gaganyaan programme and the development of indigenous space station capabilities.

The correct answer is Damodar Valley.

Key Points

• The Damodar Valley, spread across Jharkhand and West Bengal, is one of India’s most significant coal-bearing regions.
• This valley is home to the Raniganj, Jharia, Bokaro, and Giridih coalfields, which are among the richest coal reserves in the country.
• Coal deposits in the Damodar Valley are primarily bituminous coal, which is highly sought after for its use in power generation and steel production.
• The Damodar River is often referred to as the "River of Sorrows" due to frequent flooding in the past, but it plays a pivotal role in supporting the coal mining industries in the region.
• The Damodar Valley Corporation (DVC), established in 1948, manages the development of resources in the region, including coal mining and power generation.

Additional Information

• Tapti Valley:
• The Tapti River flows through the states of Madhya Pradesh, Maharashtra, and Gujarat.
• It is known for its fertile plains supporting the cultivation of cotton and other crops.
• However, the Tapti Valley is not associated with significant coal deposits.
• Ganga Valley:
• The Ganga River Basin is known for its extensive agricultural activities and fertile lands.
• It is one of the most densely populated regions in India and serves as a lifeline for millions.
• Despite its economic and cultural importance, the Ganga Valley is not a prominent region for coal mining or deposits.
• Brahmaputra Valley:
• The Brahmaputra Valley is located in Assam and is known for its tea plantations, oil fields, and natural gas reserves.
• It is also home to rich biodiversity and is prone to annual flooding.
• Coal deposits in this valley are not significant compared to the Damodar Valley.

The correct answer is Rajya Sabha.

Key Points

• Under Article 312 of the Indian Constitution, the Parliament can create a new All-India Service by passing a resolution in the Rajya Sabha.
• The resolution must be passed by a majority of not less than two-thirds of the members present and voting in the Rajya Sabha.
• After the Rajya Sabha passes the resolution, the Parliament enacts legislation to officially create the new All-India Service.
• All-India Services include the Indian Administrative Service (IAS), Indian Police Service (IPS), and Indian Forest Service (IFS), among others.
• These services are unique as they are recruited and trained centrally but serve both the central and state governments, ensuring uniformity in administrative practices across the nation.

Additional Information

• Lok Sabha
• The Lok Sabha, also known as the House of the People, is the lower house of the Indian Parliament.
• It plays a crucial role in the legislative process, particularly in financial matters, as money bills can only be introduced in the Lok Sabha.
• State Assemblies
• State Assemblies, or Vidhan Sabhas, are the legislative bodies of individual states in India.
• They are responsible for making laws on state subjects as listed in the State List of the Constitution.
• GST Council
• The GST Council is a constitutional body under Article 279A, responsible for making decisions related to the Goods and Services Tax (GST).
• It is chaired by the Union Finance Minister and includes representatives from all states and union territories.

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

Key Points

• Third Launch Pad (TLP): The Indian Space Research Organisation (ISRO) is actively working on the development of a Third Launch Pad at the Satish Dhawan Space Centre (SDSC-SHAR), located at Sriharikota, Andhra Pradesh.
• Purpose of TLP: The TLP is being designed to enhance India's space exploration capabilities by accommodating heavier and next-generation launch vehicles, such as the NGLV (Next-Generation Launch Vehicle).
• Increased Launch Frequency: The TLP will allow ISRO to increase the frequency of satellite launches, thereby contributing to India’s growing presence in the global space sector.
• Support for Advanced Missions: The new launch pad will also support advanced missions like human spaceflights under the Gaganyaan program and interplanetary missions.
• Strategic Importance: This development aligns with India’s long-term strategic goals of becoming a global leader in space exploration and satellite launches, contributing to economic growth and technological advancements.

Additional Information

• Next-Generation Launch Vehicle (NGLV):
• NGLV is being developed by ISRO as a cost-effective, three-stage rocket designed for a variety of missions, including commercial satellite launches, deep-space exploration, and human spaceflight missions.
• The vehicle will use advanced technology, including semi-cryogenic engines, to achieve higher payload capacities and efficiency.
• Satish Dhawan Space Centre (SDSC-SHAR):
• SDSC-SHAR, located in Sriharikota, serves as ISRO’s primary launch site for all satellite and space missions.
• It is equipped with two active launch pads currently, which are used for PSLV, GSLV, and other launch vehicles.
• Gaganyaan Mission:
• The Gaganyaan program is India’s maiden human spaceflight mission, aiming to send Indian astronauts (Gagannauts) into low Earth orbit.
• The Third Launch Pad will play a critical role in supporting future human spaceflights under this program.
• Space Exploration in India:
• India’s space program has evolved significantly, with notable achievements such as the Chandrayaan missions, Mars Orbiter Mission (Mangalyaan), and the Chandrayaan-3 Moon landing.
• The development of infrastructure like the TLP will further enable ISRO to expand its capabilities and collaborate on international space projects.

The correct answer is Option 1: A-B-C-D.

Key Points

• In India, a Money Bill is exclusively introduced in the Lok Sabha, as per Article 110 of the Constitution of India.
• Once introduced, the Money Bill must be passed by the Lok Sabha, where the majority support is required.
• After passage in the Lok Sabha, the bill is transmitted to the Rajya Sabha for its recommendations, but the Rajya Sabha cannot amend or reject the bill; it can only suggest changes within 14 days.
• Finally, the bill is presented to the President of India for his/her assent, which is mandatory for the bill to become a law.
• The process ensures that the Lok Sabha, as the house of elected representatives, has the final say in matters related to financial legislation.

Additional Information

• Important Facts about Money Bills:
• A bill is considered a Money Bill if it deals with taxation, borrowing of money by the government, appropriation of money out of the Consolidated Fund of India, or any matter incidental to these issues.
• The Speaker of the Lok Sabha has the final authority to decide whether a bill is a Money Bill or not.
• The Rajya Sabha cannot reject or amend a Money Bill but can suggest recommendations, which the Lok Sabha may choose to accept or reject.
• If the Rajya Sabha does not return the Money Bill within 14 days, it is deemed to have been passed by both houses in the form originally passed by the Lok Sabha.

The correct answer is Section 105.

Key Points

• Section 105 of the Bharatiya Nagarik Suraksha Samhita (BNSS) focuses on ensuring transparency and accountability in search and seizure operations conducted by law enforcement agencies.
• It mandates that all search and seizure operations should be video-recorded to ensure there is a clear record of the proceedings.
• The provision is aimed at safeguarding the rights of individuals and preventing any misuse of authority during these operations.
• Video recording serves as evidence in legal proceedings and ensures that the process is conducted fairly and in adherence to the law.
• This provision aligns with the broader objective of reforming criminal laws in India and enhancing trust between the public and law enforcement agencies.

Additional Information

• Section 50:
• Section 50 of BNSS deals with the rights of individuals during search and arrest.
• It mandates that a person being searched has the right to have the search conducted in the presence of two independent witnesses.
• This provision aims to ensure transparency and prevent any misconduct by the authorities during the search process.
• Section 62:
• Section 62 focuses on the procedural guidelines for the arrest of individuals.
• It outlines the rights of the arrested person, such as the right to be informed about the reasons for the arrest and the right to legal representation.
• It ensures that arrests are conducted lawfully and in compliance with the principles of natural justice.
• Section 176:
• Section 176 deals with the investigation of custodial deaths and disappearances.
• It mandates that such cases should be investigated by a judicial magistrate or an executive magistrate to ensure impartiality and accountability.
• This provision is crucial for addressing concerns related to custodial violence and ensuring justice for victims.
• Theme of Bharatiya Nagarik Suraksha Samhita (BNSS):
• The BNSS is a comprehensive reform of the Indian criminal laws, replacing the colonial-era Indian Penal Code (IPC), Code of Criminal Procedure (CrPC), and Indian Evidence Act.
• It aims to modernize the criminal justice system, focusing on transparency, accountability, and the protection of citizens' rights.
• The reforms emphasize the use of technology, such as video recording, to enhance the efficiency and fairness of criminal investigations and trials.

The correct answer is Department of Posts (DoP).

Key Points

• The Department of Posts (DoP) launched 'Dak Karmayogi,' an e-learning platform for its employees aimed at enhancing their skills and productivity.
• 'Dak Karmayogi' is a part of the Government of India's Digital India Initiative and aims to upskill the vast workforce of the postal department.
• This platform provides training in soft skills, technical knowledge, and leadership development to ensure better service delivery by postal employees.
• It is designed to be user-friendly and accessible, allowing employees to learn and upgrade their competencies at their own pace.
• With the introduction of 'Dak Karmayogi,' the Department of Posts aims to modernize its workforce and improve citizen-centric services across the country.

Additional Information

• Ministry of Civil Aviation (MoCA):
• This Ministry is responsible for the formulation of national policies and programs for the development and regulation of the Civil Aviation sector.
• It oversees airport infrastructure development, air navigation services, and airline operations across India.
• Key initiatives under MoCA include the UDAAN (Ude Desh ka Aam Nagrik) scheme, which aims to enhance regional air connectivity.
• Department of Fertilizers (DoF):
• The Department of Fertilizers operates under the Ministry of Chemicals and Fertilizers, focusing on the production and distribution of fertilizers across India.
• It ensures the availability of fertilizers to farmers and promotes the balanced use of nutrients to increase agricultural productivity.
• Key schemes under DoF include the Direct Benefit Transfer (DBT) system for fertilizer subsidies.
• Ministry of Housing and Urban Affairs (MoHUA):
• This Ministry is responsible for urban development, planning, and housing policies in India.
• Key initiatives under MoHUA include the Pradhan Mantri Awas Yojana (PMAY) for affordable housing and the Smart Cities Mission to promote sustainable urban living.
• It also oversees projects related to urban sanitation, such as the Swachh Bharat Mission (Urban).

The correct answer is Modernizing and digitalizing power grids and storage systems.

Key Points

• Modernizing and digitalizing power grids enhances the efficiency and reliability of energy systems by incorporating advanced technologies like smart grids and energy management systems.
• Digitalization allows for real-time monitoring, predictive maintenance, and dynamic energy optimization, enabling seamless integration of renewable energy sources into the grid.
• Upgraded storage systems such as battery energy storage solutions (BESS) and pumped hydro storage help balance energy supply and demand fluctuations caused by intermittent renewables like solar and wind power.
• The modernization of grids supports decentralized energy generation, empowering local communities to produce and consume renewable energy efficiently.
• Such advancements align with global energy transition goals, promoting the shift toward cleaner and sustainable energy systems to combat climate change.

Additional Information

• Key findings from the 2025 Energy Transition Index
• Top Performers: Sweden, Finland, Denmark, Norway, Switzerland.
• India's Performance: Ranked 71st (down from 63rd in 2024).
• India's Strengths: Improved energy efficiency, increased investment, better energy access, and emission reductions.
• India's Challenges: Need for better grid reliability, rural energy access, and reduced reliance on imported energy.
• Overall Trend: Progress in equity and sustainability has accelerated, but energy security remains a challenge, with slower readiness momentum.

The correct answer is Karnataka.

Key Points

• Dollu Kunitha is a traditional folk dance form of Karnataka performed by men using large drums known as "Dollu".
• The dance is associated with the worship of Lord Beereshwara, a form of Lord Shiva, and is prominently performed during religious and cultural events in Karnataka.
• The performers wear traditional costumes and synchronize their drum beats with rhythmic movements, creating a vibrant and energetic performance.
• This dance form is most commonly practiced by the Kuruba community of Karnataka, who have preserved this art form for centuries.
• The Dollu Kunitha performances are characterized by fast-paced rhythms, synchronized group movements, and captivating choreography, showcasing the cultural heritage of Karnataka.

Additional Information

• Andhra Pradesh
• Andhra Pradesh is renowned for its rich cultural heritage, including classical dance forms like Kuchipudi, which originated in the village of the same name.
• Folk dances like Burrakatha, Dhimsa, and Veeranatyam are popular in the region, reflecting the state's diverse traditions.
• Burrakatha is a storytelling dance form performed by a trio, narrating mythological and social stories.
• Telangana
• Telangana is known for its vibrant folk dances, including Perini Shivatandavam, which is dedicated to Lord Shiva.
• Lambadi is another popular folk dance performed by the Banjara community, showcasing their colorful attire and unique movements.
• Bathukamma, a floral festival celebrated by women, involves traditional songs and dances around flower arrangements.
• Kerala
• Kerala is famous for its classical dance forms, such as Kathakali and Mohiniyattam, which are integral to its cultural identity.
• Folk dances like Theyyam and Thiruvathirakali are widely performed, showcasing the state's traditional customs and spirituality.
• Theyyam is a ritualistic dance form that combines elaborate costumes and energetic performances, often depicting mythological stories.

The correct answer is Encourage eco-restoration through credit incentives.

Key Points

• The 'Green Credit Programme' launched in 2024 aims to incentivize environmental conservation activities, particularly eco-restoration, through credit-based mechanisms.
• It enables individuals, communities, and industries to earn credits by actively participating in activities such as afforestation, reforestation, sustainable agriculture, and waste management.
• The program is designed to promote the restoration of degraded ecosystems and enhance biodiversity while contributing to climate change mitigation.
• These credits are tradable and can be monetized, creating a financial incentive for the adoption of sustainable and eco-friendly practices.
• The initiative aligns with India’s commitments to global climate goals and its agenda of achieving sustainable development while combating environmental degradation.

Additional Information

• Renewable Energy Certificates (REC) Scheme:
• This scheme is designed to promote renewable energy generation. One REC is equivalent to one MWh of electricity generated from renewable sources and can be traded to help entities meet their renewable purchase obligations (RPO).
• National Mission for a Green India (GIM):
• Launched in 2014, this scheme focuses on afforestation activities in degraded forest areas with community participation to increase forest and tree cover and enhance forest quality.

The correct answer is Option 2.

Key Points

• India is not self-sufficient in potash-based fertilizers. The country imports almost its entire requirement of potash since it lacks significant reserves of potassium salts.
• Urea is the most commonly produced nitrogenous fertilizer in India, accounting for a significant portion of the total fertilizer production. It is widely used due to its affordability and high nitrogen content.
• Fertilizer production in India saw a significant increase after the Green Revolution in the 1960s, which focused on agricultural enhancement using high-yielding seeds, irrigation, and fertilizers.
• Gujarat and Kerala are major contributors to fertilizer production in India, contrary to the statement in the question. Gujarat is known for its production of urea and ammonia, while Kerala contributes to phosphate-based fertilizers.

Additional Information

• Fertilizer Industry in India
• India’s fertilizer industry plays a crucial role in ensuring food security by enhancing agricultural productivity.
• The industry consists of three major types of fertilizers: nitrogenous (e.g., urea), phosphatic (e.g., DAP), and potassic (e.g., MOP).
• The government provides subsidies to make fertilizers affordable for farmers, ensuring widespread adoption in agriculture.

The correct answer is Option 1.

Key Points

• Carbon credits are generated through activities like afforestation, renewable energy projects, energy efficiency improvements, and waste management projects.
• India has established a domestic voluntary carbon market, enabling businesses to trade carbon credits and achieve their emission reduction targets.
• Carbon markets globally aim to incentivize entities to reduce emissions by allowing them to trade carbon credits within a regulated framework.
• Carbon markets in India are not monitored under the Income Tax Act, 1961. They are regulated by agencies like the Bureau of Energy Efficiency (BEE) and Ministry of Environment, Forest and Climate Change (MoEFCC).
• India’s carbon market initiative aligns with its commitment to achieving net-zero emissions by 2070 under the Paris Agreement.

Additional Information

• Option 2: India has launched a domestic voluntary carbon market
• A voluntary carbon market allows entities to trade carbon credits without mandatory compliance obligations.
• India’s voluntary market includes mechanisms like the Renewable Energy Certificates (RECs) and Perform, Achieve, and Trade (PAT) scheme.
• These schemes support renewable energy generation and energy efficiency improvements, contributing to India’s emission reduction goals.
• Option 3: Carbon markets are monitored under the Income Tax Act, 1961
• Carbon markets are not governed by the Income Tax Act, 1961. Instead, they are regulated by frameworks established by environmental and energy agencies like BEE.
• The Income Tax Act primarily deals with taxation policies rather than environmental regulation.
• Theme: Carbon Markets
• Carbon markets are a mechanism to control greenhouse gas emissions by setting limits and allowing trading of emission allowances.
• They can be classified into compliance markets (regulated by law) and voluntary markets (participation is optional).
• India’s carbon market is evolving, aiming to contribute to climate goals through initiatives like the National Action Plan on Climate Change (NAPCC).

The correct answer is Son and fertility.

Key Points

• The offering of green melons during the Jawa festival by tribal girls in Jharkhand symbolizes the aspiration for fertility and the desire for sons, which is deeply rooted in tribal cultural practices.
• Jawa festival is celebrated during the harvest season and is associated with agricultural fertility and human reproduction.
• The green melon is considered a sacred object, representing new beginnings, growth, and prosperity in tribal traditions.
• The ritual of offering melons is performed with prayers and songs, emphasizing the importance of continuity and family lineage.
• It reflects the tribal community’s spiritual connection with nature and their belief in the cyclic processes of life and fertility.

Additional Information

• Major Festivals of Jharkhand:
• Sarhul: The biggest tribal festival, celebrating spring with worship of the Sal tree and village deities (Sarna Maa).
• Karam: Honors Karam Devta, the god of youth, with rituals involving the Karam tree, seeds (Jawa), dancing, and feasting.
• Sohrai: A cattle and harvest festival, coinciding with Diwali, honoring livestock like bulls, buffaloes, and goats.
• Chhath Puja: A significant four-day Hindu festival dedicated to the Sun God (Surya), involving fasting and offerings to the setting and rising sun.
• Tusu Parab/Makar: A winter harvest festival celebrated on the last day of the Poush month.

The correct answer is Option 1.

Key Points

• Inter-State Council is a constitutional body established under Article 263 of the Indian Constitution.
• It was created to facilitate coordination between the Union and State governments on matters of national importance.
• The council is primarily an advisory body and its recommendations are not binding on the Union or State governments.
• It consists of the Prime Minister as the Chairman, Chief Ministers of all States, Union Ministers, and other members as decided by the President.
• The council's primary function is to investigate and discuss subjects where coordination is required between the Union and States.

Additional Information

• Background of Article 263:
• Article 263 empowers the President of India to establish an Inter-State Council if it appears necessary for better coordination between the Union and State governments.
• The primary roles include:
• Inquiring into disputes between states.
• Discussing subjects of common interest.
• Making recommendations for policy formulation and implementation.
• Historical Development:
• The Inter-State Council was established in 1990 by a Presidential Order following the recommendations of the Sarkaria Commission.
• The Sarkaria Commission emphasized the need for a constitutional mechanism to address Union-State relations more effectively.

Shortcut Trick

Let the value of A be 100.

Since B is 25% more than A, B = 100 + 25 = 125.

Since C is 20% more than B, C = 125 + (20 / 100) × 125 = 125 + 25 = 150.

The ratio of A : C = 100 : 150 = 2 : 3.

∴ The correct answer is 2 : 3.

Alternate Method

Given:

B is 25% more than A.

C is 20% more than B.

Method Used:

Fractional representation of percentage increase.

A 100

+25%

B 125

+20%

C 150

A : C = 100 : 150 = 2 : 3

Calculations:

⇒ 25% expressed as a fraction = 1 / 4

⇒ B = A + (1 / 4) × A = 5 / 4 × A

⇒ Ratio of A / B = 4 / 5

⇒ 20% expressed as a fraction = 1 / 5

⇒ C = B + (1 / 5) × B = 6 / 5 × B

⇒ Ratio of B / C = 5 / 6

⇒ To find the overall ratio A : C, multiply the individual ratios:

⇒ A / C = (A / B) × (B / C)

⇒ A / C = (4 / 5) × (5 / 6) = 20 / 30 = 2 / 3

∴ The correct answer is 2 : 3.

Additional Information

Percentage to Fraction Conversion

Converting percentages directly to simplified fractions helps in speeding up ratio calculations. Always memorize common fractions like 25% = 1/4 and 20% = 1/5.

Compound Ratio

The compound ratio of two sequential ratios a:b and b:c is calculated by multiplying them: (a/b) × (b/c) = a/c. This provides the direct relationship between the first and last terms.

Successive Percentage Change

When a value undergoes multiple changes sequentially, you can multiply the base with successive scaling factors. For example: Final = Base × (1 + %1) × (1 + %2).

Shortcut Trick

Convert the decimal rate to a fraction for faster calculation:

0.375 L = 3/8 L

Total volume filled in 8 seconds = (3/8) × 8

Total amount = 3 L

∴ The correct answer is 3.0 L.

Alternate Method

Given:

Rate at which the machine fills water = 0.375 L/s

Total time = 8 seconds

Formula Used:

Total Volume = Rate × Time

Calculations:

⇒ Total Volume = 0.375 × 8

⇒ Total Volume = (375/1000) × 8

⇒ Total Volume = 3000/1000

⇒ Total Volume = 3.0 L

∴ The correct answer is 3.0 L.

Additional Information

Fraction to Decimal Equivalents

Memorising standard fractional values helps speed up calculations significantly. Common equivalents include: 1/8 = 0.125, 3/8 = 0.375, 5/8 = 0.625, and 7/8 = 0.875.

Unitary Method

The unitary method is a technique for solving arithmetic problems by first finding the value of a single unit (1 second in this case), and then finding the required value by multiplying the single unit value.

Work and Time Relationship

The total amount of work done or quantity processed is consistently given by the product of the rate of work and the time taken (Quantity = Rate × Time).

Shortcut Trick

Given ratio of lengths = 2/5 : 3/10 : 1/2

Multiply by LCM of denominators (10) to get integer ratio → 4 : 3 : 5

Total parts = 4 + 3 + 5 = 12 parts

Smallest piece represents 3 parts out of total 12 parts.

Length of smallest piece = (3 ÷ 12) × 6 = 1.5 m

∴ The correct answer is 1.5 m.

Alternate Method

Given:

Total length of rod = 6 m

Ratio of division = 2/5 : 3/10 : 1/2

Total Length = 6 m (12 parts)

4 parts 3 parts 5 parts

Smallest Piece = ?

Calculations:

⇒ To convert fractions into simplest integer ratio, find the LCM of denominators 5, 10, and 2.

⇒ LCM of 5, 10, 2 = 10

⇒ Multiply each fraction by 10:

⇒ First piece = 2/5 × 10 = 4 parts

⇒ Second piece = 3/10 × 10 = 3 parts

⇒ Third piece = 1/2 × 10 = 5 parts

⇒ Simplified length ratio = 4 : 3 : 5

⇒ Total ratio parts = 4 + 3 + 5 = 12 parts

⇒ Total length equivalent to 12 parts = 6 m

⇒ Value of 1 part = 6 ÷ 12 = 0.5 m

⇒ The smallest piece corresponds to the smallest ratio value, which is 3 parts.

⇒ Length of smallest piece = 3 × 0.5 m = 1.5 m

∴ The correct answer is 1.5 m.

Additional Information

Simplifying Fractional Ratios

Always multiply each term of a fractional ratio by the Least Common Multiple (LCM) of their denominators to easily convert them into standard integers.

Dividing Quantity in a Given Ratio

If a total quantity T is divided in the ratio a : b : c, the individual value of the first segment is calculated as (a ÷ (a + b + c)) × T.

Inverse Ratio Property

The inverse ratio of a : b is given as 1/a : 1/b, which simplifies mathematically to b : a. For three continuous terms a : b : c, the respective inverse ratio is expressed as 1/a : 1/b : 1/c.

Shortcut TrickCost Price per kg of mixture = (120 × 1 + 180 × 2) ÷ (1 + 2)⇒ CP = (120 + 360) ÷ 3 = 480 ÷ 3 = ₹160Given Selling Price (SP) = ₹152Loss = CP − SP = 160 − 152 = ₹8Loss % = (8 ÷ 160) × 100 = 5%∴ The correct answer is 5% Loss.Alternate MethodGiven:Cost of 1st type of coffee = ₹120 per kgCost of 2nd type of coffee = ₹180 per kgRatio of mixing = 1 : 2Selling Price (SP) of mixture = ₹152 per kgFormula Used:Total Cost Price (CP) = (Q1 × P1) + (Q2 × P2)Loss % = (Loss ÷ CP) × 100₹ 120Type 1 Cost₹ 180Type 2 Cost1Ratio Part2Ratio PartCP = ₹ 160SP = ₹ 152 → Loss = ₹ 8 (5%)Calculations:Let the quantities mixed be 1 kg and 2 kg respectively.⇒ Total CP of 3 kg mixture = (1 × 120) + (2 × 180)⇒ Total CP = 120 + 360 = ₹480⇒ CP per kg = 480 ÷ 3 = ₹160⇒ SP per kg is given as ₹152.⇒ Since SP < CP, there is a loss in the transaction.⇒ Loss per kg = 160 − 152 = ₹8⇒ Loss % = (8 ÷ 160) × 100⇒ Loss % = (1 ÷ 20) × 100 = 5%∴ The correct answer is 5% Loss.Additional InformationAlligation RuleWhen two ingredients of different prices are mixed, the ratio of their quantities is determined using: (Cheaper Qty) ÷ (Dearer Qty) = (Cost of Dearer − Mean Price) ÷ (Mean Price − Cost of Cheaper).Profit and LossProfit occurs when Selling Price > Cost Price (Profit % = Profit ÷ CP × 100). Loss occurs when Cost Price > Selling Price (Loss % = Loss ÷ CP × 100).

Shortcut Trick

Profit ratio = Capital ratio (since time is identical for all partners).

Ratio of A : B : C = 40,000 : 60,000 : 1,00,000 = 2 : 3 : 5.

Total profit ratio parts = 2 + 3 + 5 = 10 parts.

10 parts = ₹40,000 ⇒ 1 part = ₹4,000.

A's share = 2 parts = 2 × ₹4,000 = ₹8,000.

∴ The correct answer is ₹8,000.

Alternate Method

Investment & Profit Ratio

₹40k Ratio: 2 A

₹60k Ratio: 3 B

₹100k Ratio: 5 C

Total Profit = ₹40,000 (10 Ratio Units)

Given:

Investment of A = ₹40,000

Investment of B = ₹60,000

Investment of C = ₹1,00,000

Total Profit at the end of the year = ₹40,000

Formula Used:

Profit Ratio = (Capital of A × Time) : (Capital of B × Time) : (Capital of C × Time)

Calculations:

⇒ Since the time period is 1 year for all, the profit ratio relies entirely on their initial investments.

⇒ Profit Ratio of A, B, and C = 40,000 : 60,000 : 1,00,000

⇒ Dividing each term by 20,000, we get the simplified ratio = 2 : 3 : 5

⇒ Sum of profit ratios = 2 + 3 + 5 = 10 units

⇒ Total profit representing 10 units = ₹40,000

⇒ 1 unit of profit = 40,000 ÷ 10 = ₹4,000

⇒ A's share of profit is 2 units.

⇒ A's share = 2 × 4,000 = ₹8,000

∴ The correct answer is ₹8,000.

Additional Information

Simple Partnership

When all partners invest their capital for the exact same time period, their profits or losses are distributed directly in the ratio of their invested amounts.

Compound Partnership

When partners invest their capital for different time periods, the profit ratio is determined by the product of their respective capital and the total time it was invested (Profit = Capital × Time).

Sleeping Partner

A sleeping partner provides capital but does not actively participate in running the business. Their share of the profit is generated purely based on the financial investment ratio.

Working Partner

An active partner who manages the daily operations of the business. They often receive a fixed salary or a specific percentage of the total profit for their management before the rest of the profits are divided.

Shortcut Trick

Convert all animals into equivalent cows: 1 horse = 2.5 cows, and 3 sheep = 1 cow.

A's usage = (20 × 2.5) cows × 5 months = 250 cow-months.

B's usage = (30 cows × 4 months) + (45 ÷ 3) cows × 5 months = 120 + 75 = 195 cow-months.

Total equivalent usage = 250 + 195 = 445 cow-months.

A's rent portion = A's usage ÷ Total usage = 250 ÷ 445 = 50/89.

∴ The correct answer is 50/89.

Alternate Method

Given:

⇒ A uses 20 horses for 5 months.

⇒ B uses 30 cows for 4 months and 45 sheep for 5 months.

⇒ Conversion rates: 2 horses = 5 cows, and 3 cows = 9 sheep.

Formula Used:

⇒ Portion of Rent = (Individual Equivalent Usage) ÷ (Total Equivalent Usage)

Equivalent Cow-Months Usage

A: 250 units

B: 195 units Share: 250 / 445 = 50 / 89 Share: 195 / 445 = 39 / 89

Calculations:

⇒ Determine equivalent cow units for A:

⇒ 2 horses = 5 cows ⇒ 20 horses = (5 ÷ 2) × 20 = 50 cows.

⇒ A's total usage = 50 cows × 5 months = 250 cow-months.

⇒ Determine equivalent cow units for B:

⇒ 9 sheep = 3 cows ⇒ 45 sheep = (3 ÷ 9) × 45 = 15 cows.

⇒ B's usage from cows = 30 cows × 4 months = 120 cow-months.

⇒ B's usage from sheep = 15 cows × 5 months = 75 cow-months.

⇒ B's total usage = 120 + 75 = 195 cow-months.

⇒ Total usage by A and B = 250 + 195 = 445 cow-months.

⇒ A's portion = 250 ÷ 445.

⇒ Simplify the fraction by dividing numerator and denominator by 5:

⇒ 250 ÷ 5 = 50

⇒ 445 ÷ 5 = 89

⇒ A's Portion = 50/89

∴ The correct answer is 50/89.

Additional Information

Partnership in Renting

When individuals share a rented property or field, the rent must be divided proportionally based on both the amount of resources used and the time duration (Usage × Time).

Animal Equivalence

When multiple entity types are involved (horses, cows, sheep), convert all of them into a single common base unit before calculating the total usage to ensure a uniform scale.

Compound Ratio

The final ratio of share is a compound ratio formed by multiplying the equivalent units ratio and the time ratio for each individual.

Shortcut Trick

A invests 2 times more than B ⇒ Initial capital ratio A : B = 3 : 1.

A's profit units = (3 × 8) + (1.5 × 4) = 30; B's profit units = (1 × 8) + (3 × 4) = 20.

Profit ratio A : B = 30 : 20 = 3 : 2.

A's share = [3 ÷ (3 + 2)] × 75000 = ₹45,000.

∴ The correct answer is ₹45,000.

Alternate Method

Given:

⇒ Total profit after one year (12 months) = ₹75,000

⇒ A invests 2 times more than B initially.

Formula Used:

⇒ Profit Ratio = (Capital × Time)

A 8 mo × 3x 4 mo × 1.5x Sum = 30x B 8 mo × 1x 4 mo × 3x Sum = 20x Profit Ratio (A : B) = 30x : 20x = 3 : 2

Calculations:

⇒ Let B's initial investment be x.

⇒ A invests 2 times more than B, so A's initial investment = x + 2x = 3x.

⇒ For the first 8 months, A's capital is 3x and B's capital is x.

⇒ For the remaining 4 months, A withdraws half of his capital, so A's new capital = 3x ÷ 2 = 1.5x.

⇒ For the remaining 4 months, B triples his capital, so B's new capital = 3 × x = 3x.

⇒ A's profit equivalent = (3x × 8) + (1.5x × 4) = 24x + 6x = 30x.

⇒ B's profit equivalent = (x × 8) + (3x × 4) = 8x + 12x = 20x.

⇒ Profit Ratio of A : B = 30x : 20x = 3 : 2.

⇒ Total ratio parts = 3 + 2 = 5 parts.

⇒ A's share = (3 ÷ 5) × 75000 = 3 × 15000

⇒ A's share = ₹45,000.

∴ The correct answer is ₹45,000.

Additional Information

Partnership Core Principle

Profit is exclusively distributed among partners in the ratio of their effective investments (the product of capital and duration). Key formula: Profit Ratio = C₁T₁ : C₂T₂.

"More Than" Phrasing Concept

When a question states "A is n times more than B", the expression evaluates to A = B + nB. It must not be confused with "A is n times of B" which simply means A = nB.

Active vs Sleeping Partner

An active partner actively works for the business and typically claims a salary or fixed percentage of total profit before the remainder is split purely based on the initial capital-time ratio among all partners.

Shortcut Trick

Ratio of Senior Staff to Other Employees = 8 : 16 = 1 : 2

Deviation of senior staff average = ₹60,000 − ₹40,000 = +20,000

Total deviation of senior staff (1 unit) = 1 × 20,000 = +20,000

To balance the average, the other employees (2 units) must have a deviation of −20,000 ÷ 2 = −10,000

Average salary of other employees = ₹40,000 − 10,000 = ₹30,000

∴ The correct answer is ₹30,000.

Alternate Method

Given:

Total number of employees = 24

Average salary of all employees = ₹40,000

Number of senior staff = 8

Average salary of senior staff = ₹60,000

8 Senior Staff Avg: ₹60,000

16 Other Employees Avg: ₹x

Total: 24 Employees (Avg: ₹40,000)

Formula Used:

Total Salary = Average Salary × Number of Employees

Calculations:

⇒ Total salary of all 24 employees = 24 × 40,000 = ₹9,60,000

⇒ Total salary of 8 senior staff = 8 × 60,000 = ₹4,80,000

⇒ Number of other employees = 24 − 8 = 16

⇒ Total salary of 16 other employees = 9,60,000 − 4,80,000 = ₹4,80,000

⇒ Average salary of other employees = 4,80,000 ÷ 16 = ₹30,000

∴ The correct answer is ₹30,000.

Additional Information

Combined Average

When two groups of sizes n₁ and n₂ have averages A₁ and A₂, their combined average is given by (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Deviation Method in Averages

The sum of deviations of all individual values from their true average is always zero. If one group has a positive deviation, the remaining group must have an equal negative deviation to balance the overall average.

Weighted Average

Instead of calculating the total sum with large numbers, the simplified ratios of the group sizes can be used as weights to find the combined average much faster.

Shortcut Trick

When an item is excluded, its value can be calculated directly by the average deviation method:

Excluded value = Original Average + (Drop in Average × Remaining number of items)

Here, Drop in Average = 58 − 54 = 4

Excluded highest score = 58 + (4 × 9) = 58 + 36 = 94

∴ The correct answer is 94 runs.

Alternate Method

Average Score Partition

10 Innings (Average: 58)

Total Score = 10 × 58 = 580

9 Innings (Average: 54)

Total = 9 × 54 = 486

Highest Score

94

Given:

⇒ Average score of a cricketer in 10 innings = 58

⇒ Average score in 9 innings (after highest score is excluded) = 54

Formula Used:

⇒ Total Value = Average × Number of Observations

Calculations:

⇒ Total score of the cricketer in 10 innings = 10 × 58 = 580

⇒ Total score of the cricketer in 9 innings = 9 × 54 = 486

⇒ Highest score = Total score in 10 innings − Total score in 9 innings

⇒ Highest score = 580 − 486 = 94

∴ The correct answer is 94 runs.

Additional Information

Averages (Basic Concept)

Average is the central value of a set of data, calculated as the sum of all observations divided by the total number of observations.

Effect of Excluding an Observation

When an item is removed and the overall average decreases, it indicates that the value of the removed item was strictly greater than the initial average.

Combined Average

If two sets of data with n₁ and n₂ observations have averages A₁ and A₂ respectively, their combined average is (n₁ × A₁ + n₂ × A₂) ÷ (n₁ + n₂).

Shortcut Trick Since the number of rounds played by both teams is the same (3 rounds), the team with the higher total score will naturally have the higher average. Total score of Team A = 42 + 38 + 40 = 120 Total score of Team B = 45 + 46 + 44 = 135 Since 135 > 120, Team B has the higher total and thus the higher average. ∴ The correct answer is Team B.

Alternate Method Given: Scores of Team A in Round 1, 2, and 3 = 42, 38, and 40 respectively. Scores of Team B in Round 1, 2, and 3 = 45, 46, and 44 respectively. Formula Used: Average = (Sum of all observations) ÷ (Total number of observations) Calculations: ⇒ Average score of Team A = (42 + 38 + 40) ÷ 3 ⇒ Average score of Team A = 120 ÷ 3 = 40 ⇒ Average score of Team B = (45 + 46 + 44) ÷ 3 ⇒ Average score of Team B = 135 ÷ 3 = 45 ⇒ Comparing both averages, we can see that 45 > 40. ⇒ Hence, Team B has a higher average score than Team A. ∴ The correct answer is Team B.

Additional Information Average of a Set of Numbers The average (or arithmetic mean) of a set of data is found by adding all the numbers in the data set and then dividing the sum by the total number of values in the set. Direct Comparison Method When comparing the averages of two or more groups that have the exact same number of observations, calculating the total sum alone is sufficient. The group with the highest total sum will always have the highest average. Weighted Average When observations appear with varying frequencies (or weights), the weighted average formula is used: Average = (w1x1 + w2x2 + ... + wnxn) ÷ (w1 + w2 + ... + wn).

Shortcut Trick

Total Capacity = 0.005 kl = 0.005 × 1,000,000 ml = 5,000 ml.

Empty volume = 5,000 − 3,500 = 1,500 ml.

Empty Percentage = (1,500 ÷ 5,000) × 100 = 30%.

∴ The correct answer is 30%.

Alternate Method

Given:

Filled volume of the tank = 3,500 ml

Total capacity of the tank = 0.005 kl

Formula Used:

1 kiloliter (kl) = 1,000 liters (L)

1 liter (L) = 1,000 milliliters (ml)

Percentage = (Part value ÷ Total value) × 100

Total Capacity 5000 ml

Empty = 1500 ml ( ? % )

Filled = 3500 ml

Calculations:

⇒ Total capacity = 0.005 kl = 0.005 × 1,000 × 1,000 ml

⇒ Total capacity = 5,000 ml

⇒ Empty volume = Total capacity − Filled volume

⇒ Empty volume = 5,000 − 3,500 = 1,500 ml

⇒ Percentage of empty tank = (1,500 ÷ 5,000) × 100

⇒ Percentage of empty tank = 0.3 × 100 = 30%

∴ The correct answer is 30%.

Additional Information

Unit Conversions of Volume

1 Kiloliter (kl) = 10³ Liters = 10⁶ Milliliters (ml). Always ensure all given quantities are in the exact same measurement unit before performing any arithmetic calculations.

Complementary Percentages

The sum of the percentage of the filled portion and the empty portion of a container is always exactly 100%. If a tank is 70% full, it is fundamentally 100% − 70% = 30% empty.

Percentage Calculation Rule

To calculate what percentage quantity X is of quantity Y, use the standard formula: (X ÷ Y) × 100. The base reference value (Total Capacity) must always reside in the denominator.

Shortcut Trick

Let the price of standard and premium pens be 1 and 2 units respectively, and standard boxes ordered be y.

Original Cost = (8 × 2) + (y × 1) = 16 + y

New Cost (after interchange) = (y × 2) + (8 × 1) = 2y + 8

Given a 25% increase in the bill, the multiplier is 5/4, giving: (2y + 8) / (16 + y) = 5 / 4

⇒ 8y + 32 = 5y + 80 ⇒ 3y = 48 ⇒ y = 16

Ratio of Premium to Standard = 8 : 16 = 1 : 2.

∴ The correct answer is 1 : 2.

Alternate Method

Given:

Original number of premium boxes = 8

Price of a premium box is twice the price of a standard box.

New total bill is 25% more than the original bill due to interchanged quantities.

Original Bill (100%)

16 + y

New Bill (125%)

2y + 8

• 25% Increase

Calculations:

⇒ Let the original number of standard pen boxes be y and price per standard box be P.

⇒ Price per premium box = 2P.

⇒ Original Bill = (8 × 2P) + (y × P) = P(16 + y)

⇒ When quantities are interchanged, there are y premium boxes and 8 standard boxes.

⇒ New Bill = (y × 2P) + (8 × P) = P(2y + 8)

⇒ The new bill is 25% more than the original, so New Bill = 1.25 × Original Bill

⇒ P(2y + 8) = 1.25 × P(16 + y)

⇒ 2y + 8 = 1.25 × (16 + y)

⇒ 2y + 8 = 20 + 1.25y

⇒ 2y − 1.25y = 20 − 8

⇒ 0.75y = 12

⇒ y = 12 ÷ 0.75 = 16

⇒ Original number of standard pen boxes = 16.

⇒ Required ratio (Premium boxes : Standard boxes) = 8 : 16 = 1 : 2.

∴ The correct answer is 1 : 2.

Additional Information

Ratio & Proportion

A ratio compares values, showing how much of one there is compared to another. If two quantities are in the ratio a:b, they can be represented directly as ax and bx for calculation purposes to quickly establish a relation.

Percentage Increase

When a quantity increases by R%, its new value becomes (100 + R)% of the original. An increase of 25% corresponds to a multiplying factor of 125% or 5/4.

Interchange of Quantities

When two items with original quantities x and y and respective unit prices a and b are interchanged, the net change in the total bill follows the shortcut formula: Change = (a − b)(y − x). A positive result directly indicates a percentage increase.

Shortcut Trick

Multiplying factor for 10% compound interest = 1 + 10/100 = 11/10.

Ratio of final Amount to Principal = 133100 ÷ 100000 = 1331/1000.

We know that (11/10)ⁿ = 1331/1000.

Since 11³ = 1331 and 10³ = 1000, the value of n must be 3.

∴ The correct answer is 3 years.

Alternate Method

Given:

Principal (P) = ₹1,00,000

Amount (A) = ₹1,33,100

Rate of Interest (R) = 10% compounded annually

Formula Used:

A = P × (1 + R/100)ⁿ

Start (P) 100k

Year 1 110k

Year 2 121k

Year 3 (A) 133.1k

+10%

+10%

+10%

Total Time Required = 3 Years

Calculations:

⇒ 1,33,100 = 1,00,000 × (1 + 10/100)ⁿ

⇒ 133100 ÷ 100000 = (11/10)ⁿ

⇒ 1331/1000 = (11/10)ⁿ

⇒ (11/10)³ = (11/10)ⁿ

⇒ By equating the powers on both sides, we get n = 3.

∴ The correct answer is 3 years.

Additional Information

Effective Rate of Interest

For a 10% annual rate compounded annually over 3 years, the effective percentage increase directly becomes 33.1%.

Simple Interest vs Compound Interest

For the first year, SI and CI are completely identical. From the second year onward, CI starts to grow faster because interest is also applied to the accumulated interest of the preceding years.

Half-Yearly Compounding

If the interest was compounded half-yearly instead of annually, the applied rate would be halved (R/2) and the number of calculation cycles would double (2n).

Shortcut Trick

In percentage terms, the Cost Price (CP) is always considered 100%.

The given loss is 5% of the Cost Price, which is equal to ₹125.

5% → ₹125

100% → (125 ÷ 5) × 100 = ₹2500

∴ The correct answer is ₹2500.

Alternate Method

Given:

Loss incurred = ₹125

Loss percentage = 5%

Selling Price (95%) Loss (5%)

Total Cost Price (100%)

₹125

Formula Used:

Loss % = (Loss ÷ Cost Price) × 100

Calculation:

⇒ 5 = (125 ÷ CP) × 100

⇒ 5 × CP = 12500

⇒ CP = 12500 ÷ 5

⇒ CP = 2500

∴ The correct answer is ₹2500.

Additional Information

Profit and Loss Base

Profit or Loss is always calculated on the base of Cost Price (CP) unless stated otherwise in the question.

Key Formulas

Profit % = (Profit ÷ CP) × 100 | Loss % = (Loss ÷ CP) × 100

Selling Price (SP) Evaluation

When there is a profit: SP = CP × [(100 + Profit %) ÷ 100]
When there is a loss: SP = CP × [(100 − Loss %) ÷ 100]

Shortcut Trick

Let the Cost Price (CP) be 100. With a 10% loss, the initial Selling Price Y = 90.

New Marked Price (MP) = 0.8 × Y = 0.8 × 90 = 72.

New Selling Price after 5% discount = 72 × 0.95 = 68.4.

Overall Loss = CP − New SP = 100 − 68.4 = 31.6.

Percentage Loss = (31.6 ÷ 100) × 100 = 31.6%.

∴ The correct answer is 31.6%.

Alternate Method

Given:

Initial Selling Price (SP) = Y

Loss = 10%

Marked Price (MP) = 0.8Y

Discount = 5%

Formula Used:

Cost Price (CP) = SP × [ 100 ÷ (100 − Loss%) ]

Selling Price after discount = MP × [ (100 − Discount%) ÷ 100 ]

Percentage Loss = [ (CP − SP) ÷ CP ] × 100

CP = 100 Y = 90 MP = 72 SP₂ = 68.4 −10% × 0.8 −5% Overall Loss = 100 − 68.4 = 31.6%

Calculations:

Let the Cost Price (CP) of the novel be ₹100.

⇒ Loss = 10% of CP = ₹10

⇒ Initial SP (Y) = CP − Loss = 100 − 10 = ₹90

Now, the new Marked Price (MP) is set to 0.8Y to clear old stock.

⇒ MP = 0.8 × 90 = ₹72

The bookseller gives a 5% discount on this new MP.

⇒ Discount = 5% of 72 = ₹3.6

⇒ New SP = MP − Discount = 72 − 3.6 = ₹68.4

Now, calculating the overall loss on the clearance sale with respect to the original CP:

⇒ Overall Loss = CP − New SP = 100 − 68.4 = ₹31.6

⇒ Percentage Loss = (Overall Loss ÷ CP) × 100 = (31.6 ÷ 100) × 100 = 31.6%

(Note: The exact result is 31.6%. The option 31.59% is generated if intermediate fractional steps like 10/9 are rounded early.)

∴ The correct answer is 31.6%.

Additional Information

Marked Price and Successive Discount

When discounts are applied sequentially, the effective selling price is calculated directly as MP × (1 − d₁/100) × (1 − d₂/100).

Cost Price vs Selling Price

Profit or loss is always calculated on the base Cost Price (CP) unless the question specifically directs otherwise. The general relation is given by CP = SP × [ 100 ÷ (100 ± Profit/Loss%) ].

Discount vs Loss

Discount is an amount deduced solely from the Marked Price (MP), whereas Loss is the deficit calculated against the Cost Price (CP). Offering deep discounts can frequently push the Selling Price below the Cost Price, leading to an overall loss.

Shortcut Trick

There is a direct ratio relation between Cost Price and Marked Price:

CP ÷ MP = (100 − Discount%) ÷ (100 + Profit%)

⇒ CP ÷ 800 = (100 − 12) ÷ (100 + 8)

⇒ CP = 800 × (88 ÷ 108)

⇒ CP = 17600 ÷ 27 ≈ 651.85

∴ The correct answer is ₹652.

Alternate Method

CP = ?

SP = 704

MP = 800

• 8%

− 12%

Finding CP from SP and Profit %

Given:

⇒ Marked Price (MP) = ₹800

⇒ Discount = 12%

⇒ Profit = 8%

Calculations:

⇒ Selling Price (SP) = MP × (100 − Discount%) ÷ 100

⇒ SP = 800 × (100 − 12) ÷ 100

⇒ SP = 800 × (88 ÷ 100) = ₹704

⇒ SP = CP × (100 + Profit%) ÷ 100

⇒ 704 = CP × (100 + 8) ÷ 100

⇒ 704 = CP × (108 ÷ 100)

⇒ CP = (704 × 100) ÷ 108

⇒ CP = 70400 ÷ 108 ≈ 651.85

∴ The correct answer is ₹652.

Additional Information

Marked Price & Discount

Discount is always calculated on the Marked Price. Formula: SP = MP − Discount.

Direct CP & MP Relation

A very useful formula directly connects Cost Price and Marked Price: CP/MP = (100 − D%) ÷ (100 + P%).

Successive Discount

For two successive discounts of a% and b%, the effective single discount is calculated as: a + b − (a × b) ÷ 100 %.

Shortcut Trick

Cost Price (CP) for the showroom = Profit ÷ Profit% = 4500 ÷ 30% = ₹15,000

Net multiplying factor from MP to CP = (1 − 25%) × (1 + 10%) = 0.75 × 1.10 = 0.825

Marked Price (MP) = CP ÷ Net Factor

MP = 15,000 ÷ 0.825 = 2,00,000 ÷ 11 = 18,181.818... ≈ ₹18,181.82

∴ The correct answer is ₹18,181.82.

Alternate Method

Given:

Discount offered by manufacturer = 25%

Handling fee added on discounted price = 10%

Profit earned by showroom = 30%

Profit amount = ₹4500

Formula Used:

Cost Price (CP) = Profit ÷ (Profit% ÷ 100)

Final Cost Price = MP × (1 − Discount%) × (1 + Fee%)

MP−25% Disc.+10% Fee(× 0.825)CPProfit = 30%Profit = ₹4500CP × 30% = 4500SPMP × 0.75 × 1.10 = CP

Calculations:

⇒ Showroom CP × 0.30 = 4500

⇒ Showroom CP = 4500 ÷ 0.30 = ₹15,000

Let the Marked Price be MP.

⇒ Discounted Price = MP × 0.75

⇒ Price after handling fee (Showroom CP) = MP × 0.75 × 1.10

⇒ 0.825 MP = 15,000

⇒ MP = 15,000 ÷ 0.825

⇒ MP = 1,50,00,000 ÷ 825 = 2,00,000 ÷ 11

⇒ MP = 18,181.818... ≈ ₹18,181.82

∴ The correct answer is ₹18,181.82.

Additional Information

Marked Price & Discount

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

Successive Percentage Changes

When multiple changes occur on a value, the final value is computed as Initial Value × (1 ± R₁/100) × (1 ± R₂/100). The overall percentage change is not simply the sum of individual percentages.

Profit & Loss Basics

Profit or Loss is always calculated on the Cost Price (CP) unless stated otherwise. Profit = SP − CP, and Profit% = (Profit ÷ CP) × 100.

Shortcut Trick

Use the net deviation method from the average mixture price of ₹55/kg.

Deviation of 1^st type = (45 − 55) × 1 part = −10

Deviation of 2^nd type = (60 − 55) × 2 parts = +10

Net deviation of the first two types = −10 + 10 = 0

Since the net deviation is 0, the 3^rd type must have 0 deviation to maintain the average, meaning its price is exactly ₹55.

∴ The correct answer is ₹55.00.

Alternate Method

Given:

⇒ Price of 1^st type of sugar = ₹45/kg

⇒ Price of 2^nd type of sugar = ₹60/kg

⇒ Ratio of mixtures = 1 : 2 : 3

⇒ Average price of the final mixture = ₹55/kg

⇒ Let the price of the 3^rd type of sugar be ₹x/kg.

Formula Used:

⇒ Total Value = Sum of (Quantity × Price)

Calculation:

1 part ₹45

2 parts ₹60

3 parts ₹x

=

6 parts (Mixture) ₹55

Total Cost: (1 × 45) + (2 × 60) + (3 × x) = (6 × 55) 165 + 3x = 330 ⇒ x = 55

⇒ Total quantity of the mixture = 1 + 2 + 3 = 6 parts

⇒ Total cost of the mixture = 6 × 55 = ₹330

⇒ Total cost of individual parts = (1 × 45) + (2 × 60) + (3 × x)

⇒ 45 + 120 + 3x = 330

⇒ 165 + 3x = 330

⇒ 3x = 330 − 165

⇒ 3x = 165

⇒ x = 165 ÷ 3 = 55

∴ The correct answer is ₹55.00.

Additional Information

Weighted Average Formula

Used to find the combined average when multiple groups are mixed: Average = (w₁x₁ + w₂x₂ + ... + w_nx_n) ÷ (w₁ + w₂ + ... + w_n).

Rule of Alligation

Used when two ingredients are mixed: Quantity of Cheaper / Quantity of Dearer = (Dearer Price − Mean Price) / (Mean Price − Cheaper Price).

Repeated Replacement

When 'y' units of a pure liquid are replaced by water 'n' times from a total 'x' units: Final amount of pure liquid = x × (1 − y/x)ⁿ.

Shortcut Trick

If the entire sum of ₹18,000 was invested at the lower rate of 10% p.a., the total interest generated would be ₹1,800.

The extra interest earned = ₹2,160 − ₹1,800 = ₹360.

This extra ₹360 is solely due to the additional 5% interest rate on Scheme X (since 15% − 10% = 5%).

Therefore, 5% of Scheme X investment = ₹360.

100% of Scheme X investment = ₹360 × (100 ÷ 5) = ₹7,200.

∴ The correct answer is ₹7,200.

Alternate Method

Given:

Total Principal = ₹18,000

Rate for Scheme X = 15% p.a. | Rate for Scheme Y = 10% p.a.

Total Simple Interest for 1 year = ₹2,160

Method Used:

We can find the overall combined interest rate and apply the Alligation method to determine the ratio of investments.

⇒ Overall interest rate = (Total Interest ÷ Total Principal) × 100

⇒ Overall rate = (2160 ÷ 18000) × 100 = 12%

Scheme X (15%)

Scheme Y (10%)

12%

12 − 10 = 2

15 − 12 = 3 Ratio (X : Y) = 2 : 3

Calculations:

⇒ Total ratio parts = 2 + 3 = 5 parts

⇒ 5 parts = ₹18,000

⇒ 1 part = 18000 ÷ 5 = ₹3,600

⇒ Investment in Scheme X (2 parts) = 2 × 3600 = ₹7,200

∴ The correct answer is ₹7,200.

Additional Information

Alligation Method

When an amount is divided into two components and invested at different rates, the ratio of the invested parts can be quickly found using the diagonal cross-difference between the individual component rates and the overall average rate.

Shift Method (Shortcut Trick)

This assumes the entire sum is invested at the lower percentage. The remaining unassigned extra interest corresponds directly to the percentage difference between the two rates applied only on the higher-rate amount.

Simple Interest (SI)

SI = (P × R × T) ÷ 100. Under simple interest, the principal never changes, meaning the interest accrued remains strictly constant for every equivalent time period.

Shortcut Trick

For a cone and a hemisphere with equal volumes and the same base radius (r):

⇒ (1/3) × π × r² × h = (2/3) × π × r³

⇒ h = 2r

⇒ h : r = 2 : 1

∴ The correct answer is 2 : 1.

Alternate Method

Given:

Base radius of the cone = Base radius of the hemisphere = r

Let the vertical height of the cone be h.

Volume of the cone = Volume of the hemisphere

h r Cone

r r Hemisphere

Formula Used:

⇒ Volume of a cone = (1/3) × π × r² × h

⇒ Volume of a hemisphere = (2/3) × π × r³

Calculations:

According to the given condition in the question:

⇒ (1/3) × π × r² × h = (2/3) × π × r³

Canceling out the common terms ((1/3) × π × r²) from both sides:

⇒ h = 2 × r

⇒ h / r = 2 / 1

⇒ h : r = 2 : 1

∴ The correct answer is 2 : 1.

Additional Information

Volume of a Cylinder

The volume of a cylinder with base radius r and height h is three times the volume of a cone with the identical base and height. Formula: V = π × r² × h

Total Surface Area of a Hemisphere

The total surface area encompasses both the curved surface area and the flat circular base. Formula: TSA = 3 × π × r²

Curved Surface Area of a Cone

The curved surface area relies on its slant height (l), which can be found using the Pythagorean theorem where l = √(r² + h²). Formula: CSA = π × r × l

Shortcut Trick

Ratio of areas = (Ratio of circumferences)²

Area ratio = 3² : 5² = 9 : 25

9 parts = 150 m²

25 parts = (150 ÷ 9) × 25 = 416.67 m²

Approximate area ≈ 417 m²

∴ The correct answer is 417 m².

Alternate Method

Given:

Ratio of circumferences of two circular ponds = 3 : 5

Area of the smaller pond = 150 m²

Formula Used:

Circumference of a circle = 2 × π × r

Area of a circle = π × r²

3x Smaller Pond Area = 150 m²

5x Larger Pond Area = ?

Calculations:

⇒ Ratio of circumferences = (2 × π × r₁) : (2 × π × r₂) = 3 : 5

⇒ Ratio of radii (r₁ : r₂) = 3 : 5

⇒ Ratio of their areas = (π × r₁²) : (π × r₂²) = r₁² : r₂²

⇒ Ratio of areas = 3² : 5² = 9 : 25

⇒ Let the area of the larger pond be A.

⇒ 9 / 25 = 150 / A

⇒ 9 × A = 150 × 25

⇒ 9 × A = 3750

⇒ A = 3750 ÷ 9

⇒ A = 416.66... m²

⇒ Approximating to the nearest whole number, A ≈ 417 m²

∴ The correct answer is 417 m².

Additional Information

Scaling Principle for 2D Shapes

For any two similar 2D figures, the ratio of their areas is strictly equal to the square of the ratio of their corresponding linear dimensions (e.g., radius, diameter, circumference, perimeter).

Ratio of Circumference vs Radius

Since the circumference of a circle is directly proportional to its radius (C = 2πr), the ratio of the circumferences of any two circles is exactly the same as the ratio of their radii or diameters.

Ratio of Volumes for 3D Shapes

If the objects were 3D spheres instead of 2D circles, the ratio of their volumes would be equal to the cube of the ratio of their linear dimensions (Volume Ratio = a³ : b³).

Shortcut Trick

Volume of a regular hexagonal prism = (3√3 ÷ 2) × a² × h

Given base side (a) = 6 cm and height (h) = 10 cm

Volume = (3√3 ÷ 2) × 6² × 10

Volume = (3√3 ÷ 2) × 36 × 10 = 54√3 × 10 = 540√3 cm³

∴ The correct answer is 540√3 cm³.

Alternate Method

Given:

Side of the regular hexagonal base (a) = 6 cm

Height of the prism (h) = 10 cm

Formula Used:

Area of a regular hexagon = 6 × (√3 ÷ 4) × a² = (3√3 ÷ 2) × a²

Volume of a prism = Base Area × Height

6 cm

10 cm

Regular Hexagonal Prism

Calculations:

⇒ Base Area = (3√3 ÷ 2) × (6)²

⇒ Base Area = (3√3 ÷ 2) × 36

⇒ Base Area = 54√3 cm²

⇒ Volume of the prism = 54√3 × 10

⇒ Volume = 540√3 cm³

∴ The correct answer is 540√3 cm³.

Additional Information

Volume of a Prism

The volume of any right prism is calculated by multiplying the area of its base by its height. Formula: Volume = Base Area × Height.

Area of a Regular Hexagon

A regular hexagon consists of six equilateral triangles. The area is calculated as Area = 6 × (√3 ÷ 4) × a² = (3√3 ÷ 2) × a², where 'a' is the side length.

Total Surface Area of Hexagonal Prism

The total surface area includes the lateral surface area and the areas of the two bases. Formula: TSA = (6 × a × h) + 2 × [(3√3 ÷ 2) × a²].

Shortcut Trick

Since the Circumference (C) is directly proportional to the diameter (D) as C = π × D, the circumferences will also be in Arithmetic Progression (AP).

The middle term of an AP is the exact average of the first and last terms.

C_middle = (C_smallest + C_largest) ÷ 2

C_middle = (6π + 14π) ÷ 2 = 10π cm

∴ The correct answer is 10π cm.

Alternate Method

Given:

Circumference of the smallest circle (C₁) = 6π cm

Circumference of the largest circle (C₃) = 14π cm

The diameters D₁, D₂, and D₃ are in Arithmetic Progression (AP).

Outer C = 14π cm Middle C = ? Inner C = 6π cm

Diameters in AP

Formula Used:

Circumference of a circle, C = π × D

If three values a, b, c are in AP, then 2 × b = a + c

Calculations:

⇒ D₁ = C₁ ÷ π = 6π ÷ π = 6 cm

⇒ D₃ = C₃ ÷ π = 14π ÷ π = 14 cm

⇒ Since D₁, D₂, D₃ are in AP:

⇒ 2 × D₂ = D₁ + D₃

⇒ 2 × D₂ = 6 + 14

⇒ 2 × D₂ = 20

⇒ D₂ = 10 cm

⇒ Circumference of the middle circle (C₂) = π × D₂

⇒ C₂ = π × 10 = 10π cm

∴ The correct answer is 10π cm.

Additional Information

Concentric Circles

Circles having a common center but different radii are called concentric circles. The gap region bounded by any two concentric circles is known as an annulus.

Arithmetic Progression (AP)

A sequence of numbers in which the difference between consecutive terms is constant. For terms a, b, c in AP, the middle term is the arithmetic mean: b = (a + c) ÷ 2.

Area vs. Circumference

While circumferences of circles are directly proportional to their radii (C = 2 × π × r), areas are proportional to the squares of their radii (A = π × r²). Thus, if radii are in AP, areas will not be in AP.

Shortcut Trick

Since the height of the cylinder and the holes is the same, the ratio of volumes is equal to the ratio of their base areas.

Base area of the original solid cylinder = π × 5² = 25π.

Total base area of the 4 removed holes = 4 × (π × 1²) = 4π.

Percentage of volume removed = (4π ÷ 25π) × 100.

⇒ (4 ÷ 25) × 100 = 16%.

∴ The correct answer is 16%.

Alternate Method

Given:

Radius of the solid cylinder (R) = 5 cm

Radius of each drilled hole (r) = 1 cm

Number of drilled holes = 4

Let the full height of the cylinder be h.

Formula Used:

Volume of a cylinder = πr²h

Percentage removed = (Volume removed ÷ Total original volume) × 100

R = 5 cm

r = 1 cm

Top View of the Cylinder

Calculations:

⇒ Original volume of the solid cylinder = π × R² × h = π × 5² × h = 25πh

⇒ Volume of one cylindrical hole = π × r² × h = π × 1² × h = 1πh

⇒ Total volume removed by the 4 holes = 4 × 1πh = 4πh

⇒ Percentage of volume removed = (4πh ÷ 25πh) × 100

⇒ Percentage removed = (4 ÷ 25) × 100

⇒ Percentage removed = 16%

∴ The correct answer is 16%.

Additional Information

Cylinder Volume vs Surface Area

While drilling holes decreases the overall volume of the solid cylinder, it actually increases the total surface area by exposing new inner cylindrical surfaces.

Volume of a Cylinder

The total space occupied by a right circular cylinder is universally given by V = πr²h, where r is the base radius and h is the height.

Volume of a Cone

A cone with the exact same base radius and height as a cylinder contains exactly one-third of the cylinder's volume, evaluated as V = (1 ÷ 3)πr²h.

Shortcut Trick

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

Central angle of the first sector = 135°

Central angle of the second sector = (3π ÷ 4) radians = (3 ÷ 4) × 180° = 135°

Since both central angles are equal, the areas of both sectors are identical.

Ratio of their areas = 1 : 1

∴ The correct answer is 1:1.

Alternate Method

Given:

Radius of the circle (r) = 8 cm

Central angle of the first sector (θ₁) = 135°

Central angle of the second sector (θ₂) = 3π ÷ 4 radians

Formula Used:

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

Area of a sector (in radians) = (1 ÷ 2) × θ × r²

r = 8 cm 135°

Sector 1

r = 8 cm 3π/4 rad

Sector 2

Calculations:

⇒ Area of the first sector (A₁) = (135° ÷ 360°) × π × (8)²

⇒ A₁ = (3 ÷ 8) × 64π = 24π cm²

⇒ Area of the second sector (A₂) = (1 ÷ 2) × (3π ÷ 4) × (8)²

⇒ A₂ = (3π ÷ 8) × 64 = 24π cm²

⇒ Ratio of their areas = A₁ : A₂

⇒ Ratio = 24π : 24π = 1 : 1

∴ The correct answer is 1:1.

Additional Information

Area of a Sector

When the central angle θ is in degrees: Area = (θ ÷ 360°) × πr². When θ is in radians: Area = (1 ÷ 2) × θr².

Arc Length of a Sector

When θ is in degrees: Arc length = (θ ÷ 360°) × 2πr. When θ is in radians: Arc length = r × θ.

Angle Conversions

Degrees to Radians: Multiply the degree value by (π ÷ 180°). Radians to Degrees: Multiply the radian value by (180° ÷ π).

The correct answer is '1' i.e. Harmful.

Key Points

• The word deleterious means causing harm or damage.
• The synonym of deleterious is harmful, which matches its meaning.
• Options such as useful, comforting, and helpful are antonyms and do not fit the meaning of the word.

Correct sentence: The synonym of deleterious is harmful.

Additional Information

• Deleterious is often used to describe things that have negative effects on health, environment, or well-being.
• Example sentence: Smoking is deleterious to your health.

The correct answer is '2' i.e. Harmony .

Key Points

• The word Cacophony refers to a harsh, jarring mixture of sounds.
• The most appropriate antonym is Harmony, which means a pleasing arrangement or combination of sounds.
• Options like Noise, Dissonance, and Clamor are similar in meaning to cacophony rather than being its opposite.

Correct sentence: The antonym of cacophony is Harmony.

Additional Information

• Synonyms of Cacophony:
• Noise
• Clamor
• Dissonance
• Antonyms of Cacophony:
• Harmony
• Melody

The correct answer is '1' i.e. To act cowardly .

Key Points

• The idiom "Show the white feather" refers to an act of cowardice. Historically, the phrase originates from cockfighting, where a white feather in a bird’s tail was considered a sign of inferior breeding, symbolizing cowardice.
• It is used in everyday language to describe someone who acts in a cowardly manner.

Correct usage: The soldier was accused of showing the white feather when he refused to join the battle.

Additional Information

• Incorrect Options:
• Option 2: "To signal for help" does not align with the meaning of the idiom.
• Option 3: "To display courage" is the opposite of the intended meaning.
• Option 4: "To admit defeat gracefully" is unrelated to cowardice.
• Always consider the historical and contextual usage of idioms when determining their meanings.

The correct answer is '2' i.e. Candor .

Key Points

• The word subterfuge refers to deceit or trickery used to achieve one's goal.
• The most appropriate antonym of subterfuge is candor, which means honesty, openness, and sincerity.
• The other options, such as chicanery, trickery, and deception, are synonyms of subterfuge, not antonyms.

Additional Information

• Synonyms of Subterfuge:
• Deception
• Trickery
• Chicanery
• Antonyms of Subterfuge:
• Candor
• Honesty
• Sincerity

The correct answer is '1' i.e. Phytoremediation .

Key Points

• The word Phytoremediation refers to the use of plants to clean up environmental pollutants.
• Among the options provided, Phytoremediation is spelled correctly.
• The other options contain spelling errors and do not represent the correct term.

Correct spelling: Phytoremediation, which is a technique used in environmental cleanup.

Additional Information

• Phytoremediation Techniques:
• Phytoextraction: Plants absorb contaminants from the soil into their tissues.
• Phytodegradation: Plants break down pollutants within their structure.
• Rhizofiltration: Plant roots absorb and filter pollutants from water.
• This method is cost-effective and environmentally friendly compared to traditional cleanup techniques.

The correct answer is '2' i.e. Cartographer.

Key Points

• The word "Cartographer" refers to a professional who is skilled in the art and science of creating maps. The term is derived from "carto," which relates to maps, and "grapher," which means one who writes or draws.
• Option 1, "Topographer," refers to someone who studies and maps the surface features of an area, which is related but not specific to the creation of maps.
• Option 3, "Geodesist," refers to a specialist in geodesy, which is the science of measuring and understanding Earth's geometric shape, orientation in space, and gravity field.
• Option 4, "Archivist," refers to someone responsible for preserving and organizing historical records and documents, which is unrelated to map-making.

Correct sentence: A professional who prepares maps is called a Cartographer.

Additional Information

• Cartography: The science or practice of drawing maps. It incorporates elements of art, science, and technology to represent the geography of an area visually.
• Applications: Cartographers play a crucial role in urban planning, resource management, navigation, and even disaster management.

The correct answer is '2' i.e. has .

Key Points

• The sentence reads: "Each of the datasets ___ been anonymized before release."
• The subject of the sentence is "each," which is singular. Therefore, the verb must also be singular.
• Among the options, "has" is the singular verb that agrees with the subject "each."
• Thus, the correct sentence is "Each of the datasets has been anonymized before release."

Correct sentence: Each of the datasets has been anonymized before release.

Additional Information

• Singular Subjects:
• Words like "each, everyone, anybody, somebody" are singular and require singular verbs.
• Examples:
• Each of the students is responsible for their homework.
• Somebody has left their bag on the table.
• Plural Subjects:
• Words like "all, both, some, many" are plural and require plural verbs.
• Examples:
• All of the students are present.
• Many people have already arrived.

The correct answer is '1' i.e. against .

Key Points

• The phrase "opted against" is commonly used to indicate a decision not to proceed with or agree to something.
• In the given sentence, the curator decided not to display the artifact due to preservation concerns. Therefore, "against" is the correct choice.
• The other options do not fit grammatically or contextually in this sentence:
• Option 2: for - "opted for" would imply choosing to display the artifact, which contradicts the intended meaning.
• Option 3: on - "opted on" is not a correct collocation in English.
• Option 4: with - "opted with" is also not a correct collocation in English.

Correct sentence: The curator opted against displaying the artifact due to preservation concerns.

Additional Information

• Collocations:
• "Opt for" is used to indicate choosing something.
• "Opt against" is used to indicate a decision not to choose or proceed with something.

The correct answer is '2' i.e. were .

Key Points

• The subject of the sentence, "Neither the editor nor the contributors," is compound, connected by "neither-nor."
• In compound subjects joined by "neither-nor," the verb agrees with the subject closest to it.
• Here, the subject closer to the verb is "contributors," which is plural.
• Hence, the verb must also be plural.

Correct sentence: Neither the editor nor the contributors were willing to accept the changes unconditionally.

Additional Information

• Subject-Verb Agreement Rule:
• If two subjects are joined by "neither-nor" or "either-or," the verb agrees with the subject closest to it.
• Example 1: Neither the teacher nor the students were present. (Here, "students" is plural, so "were" is used.)
• Example 2: Either the students or the teacher is coming. (Here, "teacher" is singular, so "is" is used.)

The correct answer is '4' i.e. "were briefed beforehand" .

Key Points

• The error lies in part '4' of the sentence: "were briefed beforehand."
• The subject "neither the chairperson nor the legal counsel" is singular because "neither...nor" refers to singular entities and connects them as a singular subject.
• The correct verb form should therefore be "was briefed beforehand" to align with the singular subject.

Correct sentence: That none of the representatives found the proposal viable is less surprising than the fact that neither the chairperson nor the legal counsel was briefed beforehand.

Additional Information

• Subject-Verb Agreement:
• When using "neither...nor," the verb agrees with the subject closest to it. However, when both subjects are singular, the verb must be singular.
• For example: "Neither the teacher nor the student was present."
• Common Errors:
• Using a plural verb ("were") with a singular subject is a frequent mistake in sentences involving "neither...nor."

The correct answer is '2' i.e. appear to have accounted .

Key Points

• The error lies in part (2) of the sentence: appear to have accounted.
• The subject of the sentence, Neither the projection of growth nor the estimation of deficit trends, is singular.
• When two subjects are joined by "neither...nor," the verb agrees with the nearest subject, which in this case is singular (estimation of deficit trends).
• Therefore, the verb should be in singular form: "appears" instead of "appear."

Correct sentence: Neither the projection of growth nor the estimation of deficit trends appears to have accounted for the liquidity constraints that small-scale enterprises face during cyclical downturns in demand.

Additional Information

• Subject-Verb Agreement Rules:
• When two subjects are joined by "neither...nor," the verb agrees with the subject closest to it.
• For example: Neither the students nor the teacher was present.
• Common Errors in Subject-Verb Agreement:
• Confusion with collective nouns, compound subjects, or phrases that separate the subject from the verb.
• Ensure the verb corresponds to the actual subject, not a nearby noun or phrase.

The correct answer is '1' i.e. Will the revised ordinance be enforced promptly by the authorities? .

Key Points

• The given sentence is in the active voice, where the subject (authorities) performs the action (enforce the revised ordinance).
• In the passive voice, the object of the active sentence becomes the subject, and the action is expressed with be + past participle.
• The verb tense in the active sentence is a question in the future tense using will. In the passive voice, the verb structure remains consistent with will + be + past participle.

Correct sentence: Will the revised ordinance be enforced promptly by the authorities?

Additional Information

• Active Voice: The subject performs the action. Example: The chef cooked the meal.
• Passive Voice: The subject receives the action. Example: The meal was cooked by the chef.
• Rules for Passive Voice Conversion:
• The object of the active sentence becomes the subject of the passive sentence.
• Use the correct form of the verb to be followed by the past participle of the main verb.
• Maintain the same tense as the active sentence.