SSC CGL 2022 Tier-I Official Paper (Held On : 01 Dec 2022 Shift 2) (Previous Year Paper)

Given:

• The image must not to be rotated

Hence, the correct answer is "Option - (2)".

Given : [{(38 × 23) - (4 ÷ 3)} + (6 - 3)] ÷ 2

So, after interchanging the signs :

⇒[{(38 - 23) + (4 × 3)} ÷ (6 + 3)] × 2

⇒[{15 + 12} ÷ (6 + 3)] × 2

⇒[27 ÷ 9] × 2

⇒3 × 2

⇒6

Hence, "6" is the correct answer.

The logic followed here is :

• First letter interchanged position with second letter.
• Third letter interchanged position with fourth letter.

So,

• GAVE ∶ AGEV

​

And,

• KEPT ∶ EKTP

​

​Similarly,

• ACID ∶

​

​Hence, "CADI" is the correct answer.

The logic followed here is :-

From the given three different cubes taking figure 2 and figure 3 ,the adjacent sides are as shown below :

As 4 is common on both figure 2 and figure 3, it is clear that 1, 3, 5 and 6 are adjacent to it and remaining number i.e., 2 will be opposite to it.

Opposite pairs:

1 → 3

2 → 4

5 → 6

So, the opposite side of "2" will be side "4".

Hence, the correct answer is "4".

Logic : (Square root of 2^nd number) × 3 = 1^st number

So,

• 12 ∶ 16

​$\sqrt{16}$ × 3 = 12

4 × 3 = 12

12 = 12 (LHS = RHS)

And,

• 24 ∶ 64

​$\sqrt{64}$ × 3 = 24

8 × 3 = 24

24 = 24 (LHS = RHS)

Similarly,

• 18 ∶ ?

​$\sqrt{x}$ × 3 = 18

​$\sqrt{x}$ = 18 ÷ 3

​$\sqrt{x}$ = 6

$x$ = $(6)^2$

$x$ = 36

Hence, "36" is the correct answer.

The figure that will replace the question mark (?) in the following figure series is shown below:

1. For small arrow : It rotating at 90° and 45°  in the anti-clockwise direction.

2. For big arrow : It rotating at 135°  in the clockwise direction.

Final series is :

Hence, ‘option - (3)’ is the correct answer.

The figure that will replace the question mark (?) in the following figure series is shown below:

1. For '

' element - Increasing odd number of '

' are positioned subsequently.

2. For '

​' element -  Rotating right 90°subsequenlty.

3) For '

' and '

' element - Neither shifting nor rotating but are positioned alternately at the same position. 

4) For '

​' element -  Number of lines are increasing subsequently.

Final series is :

Hence, ‘option - (1)’ is the correct answer.

Logic :

1. First letter → No change
2. Second letter → (4) is added to the position value according to English alphabetic series.
3. Third letter → (8) is added to the position value according to English alphabetic series.
4. Fourth letter → (14) is subtracted from the position value according to English alphabetic series.

So,

Hence, "NCWN" is the correct answer.

Logic :

1. Difference between the position value of first and second letter = 2
2. Difference between the position value of second letter and third letter = 4

So,

• Option - (1) : TVR

• Option - (2) : DFB

​

• Option - (3) : QSO

​

• Option - (4) : KGI

​

Hence, "KGI" is the correct answer.

The logic followed here is :- (2) is added to position value according to English alphabetic series.​

​So,

• JUMPED ∶ LWORGF

​

And,

• QUICKS ∶ SWKEMU

​

Similarly,

• FUZING ∶

Hence, the correct answer is "HWBKPI".

The logic is followed here:

​

Hence, the correct answer is "LO".

The least possible Venn diagram for the given statements is as shown below :

Conclusions:

I. No K is S → Follow (As no S is K. So, it is definitely true)

II. All H are K → Does not follow (As all K are H. So, it is possible but not definitely true therefore it is definitely false)

∴ Here, Only conclusion I follows.

Hence, the correct answer is "Only conclusion I follows".

Logic : (2^nd number + 3^rd number) × 2 = 1^st number

Given :

• (240, 55, 65)

​(55 + 65) × 2 = 240

120 × 2 = 240

240 = 240 (LHS = RHS)

• (320, 85, 75)

​(85 + 75) × 2 = 320

160 × 2 = 320

320 = 320 (LHS = RHS)

So,

• Option - (1) : (140, 35, 25)

​(35 + 25) × 2 = 140

60 × 2 = 140

120 ≠ 140 (LHS ≠ RHS)

• Option - (2) : (220, 90, 15)

​(90 + 15) × 2 = 220

105 × 2 = 220

210 ≠ 220 (LHS ≠ RHS)

• Option - (3) : (160, 35, 45)

​(35 + 45) × 2 = 160

80 × 2 = 160

160 = 160 (LHS = RHS)

• Option - (4) : (200, 5, 105)​

​(5 + 105) × 2 = 200

110 × 2 = 200

220 ≠ 200 (LHS ≠ RHS)

Hence, "Option - (3)" is the correct answer.

The least possible Venn diagram for the given statements is as shown below :

Conclusions:

I. Some labours are painters → Does not follow (As some doctors are painters, some doctors are labours. So, as there is no direct relation it is possible but not definitely true)

II. Some athletes are doctors → Follow (As some doctors are labours, all the labours are athletes. So, it is definitely true)

III. All the doctors are athletes → Does not follow (As some doctors are labours, all the labours are athletes. So, it is possible but not definitely true)

IV. Some athletes are painters → Does not follow (As some doctors are painters, some doctors are labours, all the labours are athletes. So, as there is no direct relation it is possible but not definitely true)

∴ Here, Only conclusion II follows.

Hence, the correct answer is "Only conclusion II follows".

Given:

• The image must not to be rotated

Hence, the correct answer is "Option - (3)".

The logic is followed here: 

(First number - Second number) = (Second number - third number) = 2

Option (1): (153 - 151 - 147)

 -  Logic does not follow. 

Option (2): (171 - 169 - 167)

 - Logic follows

Option (3): (183 - 181 - 179)

 - Logic follows

Option (4): (201 - 199 - 197)

- Logic follows

Therefore (153 - 151 - 147) is different from other options.

Hence, the correct answer is "option (1)".

Given : 150 × 15 + 14 - 9 ÷ 2 = 6

So, after interchanging two signs and two numbers :

• Option - (1) : 9, 2, -, ×

150 - 15 + 14 × 2 ÷ 9 = 6

150 - 15 + 14 × 0.22 = 6

150 + 3.08 - 15 = 6

153.08 - 15 = 6

138.08 ≠ 6 (LHS ≠ RHS)

• Option - (2) : 9, 2, ÷, ×

150 ÷ 15 + 14 - 2 × 9 = 6

10 + 14 - 2 × 9 = 6

10 + 14 - 18 = 6

24 - 18 = 6

6 = 6 (LHS = RHS)

• Option - (3) : 150, 2, ÷, -

2 × 15 + 14 ÷ 9 - 150 = 6

2 × 15 + 1.55 - 150 = 6

30 + 1.55 - 150 = 6

31.55 - 150 = 6

118 ≠ 6 (LHS ≠ RHS)

• Option - (4) : 15, 9, +, ÷

150 × 9 ÷ 14 - 15 + 2 = 6

150 × 0.64 - 15 + 2 = 6

96 + 2 - 15 = 6

98 - 15 = 6

8 ≠ 6 (LHS ≠ RHS)

Hence, "Option - (2)" is the correct answer.

The logic followed here is :- 

​So,

• 'CYTOSKELETON' is written as 'TYCKSOELENOT'

​

And,

• 'MALNUTRITION' is written as 'LAMTUNTIRNOI'

​

Similarly,

• 'ALLITERATION' is written as

Hence, the correct answer is "LLAETITARNOI".

The logic followed here is :- 

​So,

• 'PSYCHIC' is written as 'YSPCCIH'

​

And,

• 'CITIZEN' is written as 'TICINEZ'

​

Similarly,

• 'MAHATMA' is written as :

Hence, the correct answer is "HAMAAMT".

According to dictionary order :

3. Unsafe
4. Unsay
5. Unseam
6. Unseen
7. Unsound

Hence, "Unseen" is the correct answer.

Given :

So,

• Option - (1) : Q + P × R → Q is the mother of P who is the father of R.

​

Here, Q is the mother of P.

• Option - (2) : P + Q × R → P is the mother of Q who is the father of R.

​

Here, Q is the son of P.

• Option - (3) : R × Q + P → R is the father of Q who is the mother of P.

​

Here, Q is the mother of P.

• Option - (4) : P + Q + R → P is the mother of Q who is the mother of R.

​

Here, Q is the daughter of P.

Thus, only option - (2), 'P + Q × R' shows that Q is the son of P.

Hence, "Option - (2)" is the correct answer.

Given : 30 ÷ 6 × 4 + 15 - 35 = 25

So, after interchanging two signs and two numbers :

• Option - (1) : 25 and 30, × and -

25 ÷ 6 - 4 + 15 × 35 = 30

4.16 - 4 + 15 × 35 = 30

4.16 + 525 - 4 = 30

 

529.16 - 4 = 30

525.16 ≠ 30 (LHS ≠ RHS)

• Option - (2) : 4 and 6, + and -

30 ÷ 4 × 6 - 15 + 35 = 25

7.5 × 6 - 15 + 35 = 25

45 + 35 - 15 = 25

80 - 15 = 25

65 ≠ 25 (LHS ≠ RHS)

• Option - (3) : 25 and 35, × and ÷

30 × 6 ÷ 4 + 15 - 25 = 35

30 × 1.5 + 15 - 25 = 35

45 + 15 - 25 = 35

60 - 25 = 35

35 = 35 (LHS = RHS)

• Option - (4) : 30 and 35, - and ÷

35 - 6 × 4 + 15 ÷ 30 = 25

35 - 6 × 4 + 0.5 = 25

35 + 0.5 - 24 = 25

35.05 - 24 = 25

11.05 ≠ 25 (LHS ≠ RHS)

Hence, "Option - (3)" is the correct answer.

Given : 

Statement : A + G & I + R @ S @ T # U & V

So, according to the given symbols :​

• A + G → A is the father of G.

​

• G & I → G is the brother of I.

​

• I + R → I is father of R.

​

• R @ S → R is he sister of S.

​

• S @ T → S is the sister of T.

​

• T # U → T is the wife of U.

​

• U & V → U is the brother of V.​

Thus, according to the final family tree :

• Option - (1) : I is the father-in-law of U → Correct
• Option - (2) : A is the maternal grandfather of T → Incorrect
• Option - (3) : G is the brother of I → Correct
• Option - (4) : R is the paternal granddaughter of A → Correct

Hence, "Option - (2)" is the correct answer.

Logic : (1^st number ÷ 5 ) = (2^nd number ÷ 3)  

So, 

• 35 ∶ 21

35 ÷ 5 =  21 ÷ 3

7 = 7 (LHS = RHS)

And,

• 40 ∶ 24

40 ÷ 5 =  24 ÷ 3

8 = 8 (LHS = RHS)

Similarly,

• ? ∶ 36

$x$ ÷ 5 =  36 ÷ 3

$x$ = 12 × 5

$x$ = 60

Hence, "60" is the correct answer.

The logic followed here is : Alternate addition of (2) and Multiplication by (2).

⇒4 + 2 = 6

⇒6 × 2 = 12

⇒12 + 2 = 14

⇒14 × 2 = 28

⇒28 + 2 = 30

⇒30 × 2 = 60

Hence, "60" is the correct answer.

The correct answer is Public 

 Key Points

• The general definition of the public sector includes government ownership or control rather than mere function and thereby includes, for example, the exercise of public authority or the implementation of public policy.
• PSUs (Public Sector Undertakings) are government-owned corporations in India, in which 51% or more than 51% of the paid-up share capital is owned by the government of India.
• However, it can be only the central government or only state government of any state or central government with any state government or state governments.

 Important PointsPublic Sector undertakings (PSU) can be classified into three following categories:

• Central public-sector Enterprises (CPSEs) – Companies that are under the direct control of the Central Government or of other CPSEs by 51% or more than 51% of capital share ownership.
• Central Public-Sector Enterprises (CPSEs) are further classified into Strategic CPSE and Non-strategic CPSE.
• Strategic Central Public-sector Enterprises (CPSEs) which includes the Arms & Ammunition and the defense equipment’s, defense aircraft and other items related to Defense, and in the field of atomic energy and Railways transport.
• The rest of the CPSEs are regarded as Non-strategic CPSE.
• Public Sector banks (PSBs) – Banks that are under the direct control of the Central Government or of other PSBs by 51% or more than 51% of capital share ownership.
• State Level Public Enterprises (SLPEs) – Companies that are under the direct control of the State Government or other SLPEs by 51% or more than 51% of capital share ownership.

The correct answer is Banaras.

Key Points

• The Hindu college was established in 1791 to encourage the study of ancient Sanskrit texts.
• Sri Jonathan Duncan and Governor General Lord Cornwallis established the Sanskrit college.
• Jonathan Duncan suggested establishing a Sanskrit college to develop and preserve Sanskrit Vangmaya to demonstrate British support for Indian education.
• The Governor of Uttar Pradesh is the chancellor of the College.
• Chancellor - Anandiben Patel
• Vice Chairman - Hare Ram Tripathi

Confusion Points

• Hindu college, now called Presidency University, is a public state university in Calcutta.
• It was established in the year 1817.

Additional Information

• In 1958 The Sanskrit college became a university and in 1974 the name was changed to  Sampumanand  Sanskrit University.
• It became a university on 22 March 1958 by the then Chief Minister Dr Sampurnanand and Education Minister Pt. Kamlapati Tripathi at Varanasi.
• A.N. Jha was the First Vice-Chancellor. It Was Renamed Sampurnanand Sanskrit University under the U.P. State University Act, of 1973.
• Introduction of Civil service by Lord Cornwallis.
• Permanent Settlement 1793 by Lord Cornwallis.
• Kumar Gupta I of the Gupta dynasty founded Nalanda University in the 5^th century CE.
• Dharmapala founded Vikramshila University.

The correct answer is Marathi

Key Points 

• The Gulamgiri by Mahatma Jyotiba Phule is regarded as one of the earliest tracts opposing the caste system.
• It was written in 1873 in Marathi language
• In 1885, it was published.
• It uses a 16-part essay and four lyrical pieces to criticise the caste system.
• It is written as a conversation between a character named Dhondiba and Jotiba.

Additional Information 

• Jyotiba Phule (11 April 1827 – 28 November 1890) was a Maharashtra-born Indian social reformer, writer, and anti-caste crusader.
• He and his wife, Savitribai Phule, were forerunners in India when it came to women's education.
• In 1848, Phule established his first girls-only school in Pune in Tatyasaheb Bhide's house, also known as Bhidewada.
• In order to secure equal rights for members of lower castes, he founded the Satyashodhak Samaj (Society of Truth Seekers) along with his adherents.

The correct answer is Barley and gram

Key Points 

• Rabi crops are winter-planted crops that are harvested in the spring.
• Rabi crops are sown in winter from October to December and harvested in summer from April to June.
• Wheat, barley, gram, peas, and lentils are among them.
• A warm climate is required for seed germination and a cold climate for the growth of crops.

Additional Information 

Kharif crop :

• Crops that are sown during the southwest monsoon season are called Kharif or monsoon crops.
• These crops are sown at the beginning of the season around the end of May to early June and are harvested post the monsoon rains beginning in October.
• Rice, maize, pulses such as urad, moong dal and millets are among the key kharif crops.
• It requires a lot of water and hot weather to grow.

Zaid Crop :

• Sown and harvested: March-July (between Rabi and Kharif)
• Important Zaid crops include: Seasonal fruits, vegetables, fodder crops etc.

The correct answer is Zooplankton

Key PointsZooplankton:

• Zooplankton is the common name given to many small species of animals found in fresh and marine waters throughout the world.
• The word zooplankton, derived from Greek, means "wandering animals."
• They float in the water column and drift with the currents. Most of these animals are so minute they are visible only with a microscope, although some species can reach lengths of eight feet.
• Two general groups of zooplankton exist those that remain planktonic throughout their entire life (holoplankton), and those that are larval stages of larger life forms (meroplankton).
• Some examples of zooplankton are Krill, jellyfish, Portuguese man o' war, squid, etc.

Important Points 

Phytoplanktons:

• Derived from the Greek words phyto (plant) and plankton (made to wander or drift), phytoplankton are microscopic organisms that live in watery environments, both salty and fresh.
• Some phytoplankton are bacteria, some are protists, and most are single-celled plants.
• Among the common kinds are cyanobacteria, silica-encased diatoms, dinoflagellates, green algae, and chalk-coated coccolithophores.

The correct answer is Wuhan, China.

Key Points

• The 7^th CISM World Games, 2019 were held in Wuhan, China.
• The military games were played from 18 to 27 October 2019 under the motto Military Glory, World Peace.
• It was the first International military multi-sport game held in China,
• This event occurs once in four years.
• The standing was topped by China and the rank of India was 27.

Additional Information

• ​CISM MILITARY WORLD GAMES
• The Military World Games are a multi-sports event organized by different nations every four years, one year before the year the Olympic Games are organized.
• The first Games took place to celebrate the 50^th anniversary of the end of the second World War.
• Bogota is set to hold the 2023 Military Games.
• CISM -  International Military Sports Council.

The correct answer is Kirana Gharana.

Key Points

• Abdul Karim Khan was the founder of the Kirana Gharana of classical music.
• Kirana Gharana is one of the most prominent Indian classical khayal gharanas and is associated mostly with the perfect intonation of notes.
• The Gharana style was further evolved and was established as one of the important styles in modern Indian classical music in the late 19^th /early 20^th centuries by the musicians Abdul Karim Khan and Abdul Wahid Khan.
• The name of this school of music comes from Kirana or Kairana, a town and tehsil of Shamli District in Uttar Pradesh.

Additional Information

The correct answer is Nitish Kumar.

Key Points

• Nitish Kumar on 10 August 2022 took oath as the Bihar chief minister for the eighth time.
• Nitish Kumar has earlier served as the Union Minister under PM Atal Bihari Vajpayee.
• Tejashwi Yadav was also administered the oath of office as deputy CM in a ceremony at Raj Bhawan.​

Additional Information

• Bihar:
• Capital: Patna
• Governor: Rajendra Vishwanath Arlekar
• Lok Sabha seats - 40.
• Rajya Sabha seats - 16.
• State Animal - Gaur.
• State Bird - House sparrow.
• National Park - Valmiki National Park.

The correct answer is In the M phase, the cell grows physically larger and copies organelles.

Key Points

• The ordered sequence of events that occur in a cell in preparation for cell division is called the cell cycle.
• The cell cycle is divided into two phases:
• Interphase
• M Phase
• The M Phase represents the phase when the actual cell division occurs.
• The Interphase represents the phase between two successive M phases.

Additional Information

• The Interphase is divided into three further phases;
• G1 Phase
• S Phase
• G2 Phase
• During the G1 phase, the cell is metabolically active and continuously grows but does not replicate its DNA.
• S or Synthesis phase marks the period during which DNA synthesis or replication takes place
• During the G2 phase, proteins are synthesized in preparation for mitosis while cell growth continues.

The correct answer is London.

Key Points

• Shyamji Krishna Varma started the India house in London, in 1905.
• India House was a student residence at Cromwell Avenue in Highgate, North London.
• Shyamji Krishna Varma is an Indian patriot, lawyer, and, journalist.
• Founder of the Indian Home Rule Society, India House, and The Indian Sociologist in London.
• He founded the India House and The Indian Sociologist In 1905.
• The Indian Sociologist was an Indian nationalist journal.
• Shyamji inaugurated a new organization called The Indian Home Rule Society, On 18 February 1905.

The correct answer is Rajasthan.

Key Points

• The Rajasthan government has come up with the job description under its much-touted Indira Gandhi Shahri Rozgar Guarantee Yojana.
• Announcing the employment scheme for urban areas on the lines of MGNREGA for rural areas in the budget speech
• While MGNREGA assists people in rural areas, there is no such scheme for street vendors, as well as those working at dhabas and restaurants in urban areas.​

Additional Information

Indira Gandhi Shahri Rozgar Guarantee Yojana:

• Under the scheme, 100 days of employment per year will be provided to families residing in urban areas.
• The ratio of cost of material to pay for labour work of “general nature” will be in the ratio of 25:75, while for special works, it will be 75:25.

Eligibility:

• All those aged between 18 and 60 years and residing within urban body limits are eligible for the scheme, and in special circumstances such as a pandemic or a calamity, migrant labourers may be included.

The correct answer is Fourth Five-year Plan - Family planning programme

Key Points

• Fourth Five-Year Plan (1969-1974)
• The fourth Five Year Plan was the first plan launched by the Indira Gandhi government amid the pressure of drought, devaluation, and inflationary recession.
• The country was fighting with population explosion, increased unemployment, poverty, and a shackling economy. In addition, the situation in East Pakistan (now independent Bangladesh) was becoming dire as the Indo-Pakistani War of 1971 and the Bangladesh Liberation War took place.
• Funds earmarked for industrial development had to be used for the war effort.
• The result was that this plan period was also no better than the third five-year plan.
• It gave emphasis on Family planning programs to control the population.​

Additional Information

The correct answer is Indira Gandhi.

Key Points

• It was added to the Constitution of India under the leadership of Indira Gandhi.
• The Fundamental Duties of citizens were added to the Constitution by the 42^nd Amendment in 1976, upon the recommendations of the Swaran Singh Committee that was constituted by the Government.
• When the Constitution was adopted in the year 1949, there were no provisions regarding Fundamental Duties to the Citizens though there was a Part III for Fundamental Rights.
• The Swaran Singh Committee suggested that steps needed to be taken to ensure that the individual did not overlook his duties while in the exercise of his Fundamental Rights.

Additional Information

By way of the 42^nd Constitution (Amendment) Act, 1976, a new Chapter IV-A which consists of only one Article i.e 51-A was added which dealt with a Code of Ten Fundamental Duties for citizens.

• Fundamental duties are intended to serve as a constant reminder to every citizen that while the constitution specifically conferred on them certain Fundamental Rights, it also requires citizens to observe certain basic norms of democratic conduct and democratic behavior because rights and duties are correlative.
• The inclusion of Fundamental Duties brought our Constitution in line with Article 29 (1) of the Universal Declaration of Human Rights and with provisions in several modern Constitutions of other countries.
• The concept of Fundamental duties was taken from the USSR.
• The Fundamental duties are essentially taken from Indian tradition, mythology, religions, and practices.
• Essentially these were the duties that are the codification of tasks integral to the Indian way of life.

Thus, we can conclude that Fundamental Duties were added to the Constitution of India in 1976.

The correct answer is Onam.

Key Points

• Onam is related to Kerala state.
• Onam is the largest and official festival in Kerala, an Indian state known as God’s Own Country.
• Malayali people celebrate the Onam festivals as annual harvesting.
• The Onam festival is celebrated in Kerala between August and September. ​

Additional Information

The correct answer is Delhi.

Key Points

• Delhi government on 6 July 2022 launched the ‘Mission Kushal Karmi’ programme to upgrade the skills of construction workers.
• The programme was launched by Delhi Deputy Chief Minister Manish Sisodia.
• The objective of this programme is to provide on-the-job skill development training to construction workers.
• Delhi govt aims to train 2 lakh workers in a year under this programme.

Additional Information

• The Delhi government has decided to replace the word 'Harijan' from the names of colonies and streets and rename them after Babasaheb Ambedkar instead.
• Delhi, officially the National Capital Territory (NCT) of Delhi, is a city and a union territory of India containing New Delhi, the capital of India.
• Delhi:​ 
• Lt. Governor: Vinai Kumar Saxena
• Chief Minister: Arvind Kejriwal
• Deputy Chief Minister: Manish Sisodia
• Legislature Unicameral: 70 seats
• Parliamentary constituencies: Rajya Sabha (3 seats) Lok Sabha (7 seats)

The correct answer is Singapore.

Key Points

• The 1^st Summer YOG was held in Singapore, in August 2010.
• The youth Olympic Games (YOG) is an international multi-sport event for athletes between 15 and 18 years old
• The YOG was created at the initiative of the former President of the International Olympic Committee (IOC), Jacques Rogge.
• The 1^st Winter YOG was held in Innsbruck, in January 2012.

Additional Information

• The 2020 Winter Youth Olympic Games were held in Lausanne.
• The 2024 Winter Youth Olympics will take place in Gangwon, South Korea.
• The 2026 Summer Youth Olympics will be held in Dakar, Senegal.
• International Olympic Committee
• President - Thomas Bach
• HQ - Lausanne, Switzerland

The correct answer is dry desert.

Key Points

• Thorny bushes are found in a hot and dry desert climate with seasonal rainfall averaging 250 to 500 millimetres or less than 50-70 cm.
• Thorny forests are found in the semi-arid areas of Gujarat, Rajasthan, Madhya Pradesh, Chhattisgarh, Uttar Pradesh, and Haryana.
• Acacias, palms, euphorbias, and cacti are the main plants found in these forests.
• The stems are succulent to conserve water.
• The bushes shed their leaves seasonally to avoid loss of water.
• Leaves are modified into spines (thorns) and are small to minimize transpiration.

Additional Information

• Hot desert:
• The climate of the hot desert is scorching hot and parched dry.
• It has a short rainy season, it does not show a significant seasonal effect.
• The sky is cloudless and clear.
• Here, the moisture evaporates faster than it accumulates.
• Days are unbelievably hot.
• The temperatures during the day may soar as high as 50°C, heating up the sand and the bare rocks, which in turn radiates heat making everything around hot.
• Hot Desert sand is a very faint and slightly pigmented reddish-yellow colour that closely resembles the colours of sand, so we can say that hot deserts are red or orange in colour.
• The nights may be freezing cold with temperatures nearing zero degrees.
• An example of a hot desert is Sahara.

The correct answer is Bidesiya.

Key Points

• Bidesiya is an important style of song that are sung in Baghelkhand.
• Bidesiya's songs are related to the theme of love, separation, and reunion with the beloved.
• The Bidesiya song implores the loved ones to return early.
• Baghelkhand is a region that covers the northeastern regions of Madhya Pradesh and a small area of southeastern Uttar Pradesh, also in Bhojpuri-speaking belt' comprising parts of Bihar.
• Bagelkhand is surrounded by the Indo-Gangetic plains in the north and east, Bundelkhand in the west, and the Vindhya range in the south.

Additional Information

The correct answer is Sonal Mansingh.

Key Points

• Sonal Mansingh is a prominent Indian classical dancer who specializes in Bharatnatyam and Odissi.
• In 2003, Sonal became the first Indian women dancer to be awarded Padma Vibhushan.
• She was the youngest recipient of Padma Bhushan in 1992.

Additional Information

• Kumudini Lakhia:
• She is an Indian Kathak dancer.
• She is a recipient of the Padma Shri, Padma Bhushan, and Sangeet Natak Akademi Awards.
• Shovana Narayan:
• ​She is a famous Indian Kathak dancer.
• She has been awarded the Padma Shri and Sangeet Natak Akademi Award.
• Her guru is Birju Maharaj.
• Sunayana Hazarilal:
• She is an Indian classical Kathak dancer from Janakiprasad Gharana.
• In 2011, she was awarded the fourth highest civilian award of Padma Shri.

The correct answer is m/s2

Key Points

• The international System of Units (SI), commonly known as the metric system, is the international standard for measurement.
• We can drive units of other quantities by using fundamental units:
• velocity = Velocity is defined as the rate of change in distance
• unit of velocity = unit of length/unit of time = metre/sec
• Acceleration = rate of change of the velocity
• Unit of acceleration = unit of velocity/ unit of time = metre/sec/sec = metre/sec2

Additional Information

• SI Units of Quantity:

The correct answer is three chiefs.

Key Points

• The Sangam poems mentioned the Muvendar.
• This is a Tamil word meaning three chiefs, used for the needs of three ruling families, The Cholas, Cheras and Pandyas who became powerful in south India around 2300 years ago.
• Many poets whose compositions are found in the Sangam collection composed poems in praise of chiefs who often rewarded them with precious stones, gold, horses, elephants, chariots and fine cloth.

Additional Information

• Dhamma mahamatta was the officer appointed by Ashoka. They used to go from place to place teaching people about dhamma.
• During the Mughal reign, panchayats were headed by headmen known as Muqaddam.
• The chief function of the Headmen was to supervise the preparation of village accounts,
• The Sangam Age was the period of the history of ancient south India and Sri Lanka spanning from the 1^st to 3^rd Century AD.
• Three early kingdoms of the Sangam period were The Chola , The Cheras and The Pandya.
• Cheras:
• Vanji was the capital of the Cheras Kingdom.
• The scripts and inscriptions were written in the Malayalam language.
• Cholas:
• Known as Imperial Cholas of Tanjore.
• The founder of the Chola Dynasty was Vijayalaya who was at first a feudatory of Pallavas.
• Pandyas:
• The Pandyas ruled present-day Southern Tamil Nadu.
• The Pandya kings patronized Tamil poets and scholars.

The correct answer is 5.

Key Points

• The Vice-President of India is the second highest constitutional office in the country.
• Article 63 of the Indian Constitution mentions the post of Vice-President.
• He serves for a five-year term but can continue to be in office, irrespective of the expiry of the term, until the successor assumes office.
• The Vice-President is the ex-officio Chairperson of the Council of States (Rajya Sabha) and does not hold any other office of profit.
• During any period when the Vice-President acts as or discharges the functions of the President, he does not perform the duties of the office of the Chairperson of the Council of States (Rajya Sabha) and, is not entitled to any salary or allowances payable to the Chairperson, Rajya Sabha.
• The Vice-President is elected by an electoral college consisting of members (elected and nominated) of both Houses of Parliament, in accordance with the system of proportional representation by means of the single transferable vote and the voting in such election is by secret ballot.
• The oath of office to the Vice President is administered by the President.
• Questions and disputes concerning the election of the Vice President are inquired into and decided by the Supreme Court, whose decision is final.
• The Vice-President is elected by a single transferable vote according to the proportional representation method by the electorate consisting of members of both houses of Parliament.
• Voting in such an election is secret. There are members of both houses of parliament in the constituency to elect a person for the post of Vice President.
• The Vice-President is not a member of any House of Parliament or of any House of the Legislature of a State.
• If a member of a House of Parliament or a member of a House of the Legislature of a State is elected Vice-President,
• So it is understood that he has vacated his place in that House from the date he assumed office as Vice-President.

Important Points

• The current Vice-President of India is the former Governor of West Bengal Jagdeep Dhankhar (as of 2023).

The correct answer is Anthracite.

Key Points

• Anthracite is the highest quality of hard coal.
• Anthracite is the most highly metamorphosed form of coal.
• It contains around 86% fixed carbon and 14% volatile matter.
• Anthracite considered the least plentiful form of coal.
• Coal is considered the most abundantly available fossil fuel.
• It provides a substantial part of the nation’s energy needs.
• Coal is formed due to the compression of plant material over a long period of time.

Additional Information 

• Lignite is low-grade brown coal.
• Lignite is soft with high moisture content.
• The principal lignite reserves are in Neyveli in Tamil Nadu.
• Bituminous coal is the coal that has been buried deep and subjected to increased temperatures.
• Bituminous coal is the most popular coal in commercial use.
• Decaying plants in swamps produce peat coal.
• Peat has low carbon and high moisture content and low heating capacity.

The correct answer is Filament, hook and basal body.

Key Points

• Bacterium Flagella
• Bacterial flagella are made of the protein flagellin and are a coiled, thread-like structure with a sharp bend and a rotary motor at the base.
• It gives bacteria the ability to swim freely through a binary compound of aqueous, also known as motility or self-propulsion.
• It is composed of three major structural elements;
• Basal body
• It is joined to the cytoplasmic membrane and cell membrane.

It is made up of rings that are surrounded by MotB proteins.

• Hook
• A hook is a name for the wider area at the base of the flagellum.
• It connects the filament to the base's motor protein.
• Filament
• It is a thin, hair-like structure emerging from the hook.

Additional Information

• The long, helical filament of bacterial flagella is made up of several flagellin subunits organised in a variety of tangled chains.
• A flagellum is made up of numerous parts and rotates, similar to a boat motor's propeller.
• Depending on the species, the diameter of bacterial flagella varies, which lies between 15 and 20 nm.
• Functions of Bacterial Flagella
• Role in pathogenesis
• Organ of locomotion
• Role in identification of organism

The correct answer is bleaching powder.

Key Points

• Bleaching powder:
• The chlorine produced on passing electricity through brine solution undergoes a reaction with dry slaked lime [Ca (OH)2] to produce Bleaching powder.
• The reaction is as follows: Ca(OH)2 + Cl2 → CaOCl2 + H2Owhere,
• Ca(OH)2 is calcium hydroxide or dry-slaked lime.
• Cl2 is chlorine gas
• CaOCl2 is a bleaching powder or calcioxychlorate.​

Additional Information

• Bleaching powder is used for several purposes:
• As a bleaching agent for bleaching cotton and linen in the textile industry,
• To bleach wood pulp in the paper manufacturing industry.
• To bleach washed clothes in the laundry.
• As an oxidizing agent in many chemical industries.
• To disinfect drinking water and make it germ-free.

Important Points

Given:

k is a negative number such that k + k-1 = -2.

Concept used:

(a + b)² = a² + 2ab + b²

Calculation:

k + k-1 = -2

⇒ k² + 1 = -2k

⇒ k² + 2k + 1 = 0

⇒ (k + 1)² = 0

So, k = -1

Now,

$\frac{k^2+4 k-2}{k^2+k-5}$

⇒ $\frac{(-1)^2+4 \times (-1)-2}{(-1)^2+(-1)-5}$ (Putting k = -1)

⇒ $\frac{1-4-2}{1-1-5}$

⇒ $\frac{-5}{-5}$

⇒ 1

∴ The required value is 1.

Given:

$\left(x+\frac{1}{x}\right)=5 \sqrt{2}$

Concept used:

$(a + \frac {1}{a})^2 = a^2 + \frac {1}{a^2} + 2$

Calculation:

$\left(x+\frac{1}{x}\right)=5 \sqrt{2}$

⇒ $\left(x+\frac{1}{x}\right)^2={(5 \sqrt{2})}^2$

⇒ $x^2 + \frac {1}{x^2} + 2 = 50$

⇒ ${(x^2 + \frac {1}{x^2})^2} = 48^2$

⇒ ${(x^4 + \frac {1}{x^4}+ 2)} = 2304$

⇒ ${(x^4 + \frac {1}{x^4})} = 2302$

∴ The required value of ${(x^4 + \frac {1}{x^4})}$ or (x4 + x- 4) is 2302.

Given:

A man rows a boat a certain distance downstream in 9 hours, while it takes 18 hours to row the same distance upstream. ​

Concept used:

1. Distance = Speed × Time 2. While rowing upstream, the upstream speed is the difference between the speed of the boat in still water and the speed of the flow. 3. While rowing downstream, the downstream speed is the addition of the speed of the boat in still water and the speed of the flow. 4. Componendo-Dividendo Method

Calculation:

Let the distance, speed of the boat in still water, and speed of the river be D, S, and R respectively.

​According to the concept,

D/(S - R) = 18      ....(1)

D/(S + R) = 9      ....(2)

(1) ÷ (2),

(S + R)/(S - R) = 2

⇒ $\frac {S + R + S - R}{S + R - S + R} = \frac {2 + 1} {2 - 1}$ (Componendo-Dividendo Method)

⇒ $\frac {S}{R} = 3$

⇒ S = 3R

Putting S = 3R in (1), D = 36R

Now, time taken to row three-fifth of the same distance in still water = $36R \times \frac {3}{5} \div 3R$ = 7.2 hours

∴ It will take 7.2 hours to row three-fifth of the same distance in still water.

Shortcut Trick

Let's assume the total distance be 180 km

So, down-stream speed will be 180/9 = 20 km/hr

So, up-stream speed will be 180/18 = 10 km/hr

Now, speed of the boat will be (20 + 10)/2 = 15 km/hr

So,the boat can row (3/5^th of 180km) 108 km in 108/15 = 7.2 hr

Calculation:

Percentage of Kerala in total production = $\frac {200}{220 + 240 + 180 + 160 + 200} \times 100$ = 20%

We know that 100% of the pie chart represents 360°.

Now, the 20% pie chart represents = $\frac {360 \times 20}{100}$ = 72°

∴ The central angle corresponding to the production of steel by Kerala is 72°.

Shortcut Trick

Let Cost Price (CP) = 100, then Selling Price (SP) = 144 (since 44% profit).

Equivalent discount for 10% and 20% successive discounts = 10 + 20 − (10 × 20)/100 = 28%.

Marked Price (MP) = 144 ÷ (1 − 0.28) = 144 ÷ 0.72 = 200.

New Selling Price at 15% discount = 200 × (1 − 0.15) = 200 × 0.85 = 170.

Net Profit % = ((170 − 100) ÷ 100) × 100 = 70%.

∴ The correct answer is 70%.

Alternate Method

-28% Equivalent Discount

-15% Discount

+44% Profit

+70% Net Profit

CP=100

SP1=144

SP2=170

MP=200

Given:

Net profit with successive discounts of 10% and 20% = 44%

New discount percentage = 15%

Formula Used:

Equivalent Discount = D₁ + D₂ − (D₁ × D₂) ÷ 100

MP = (SP × 100) ÷ (100 − Discount %)

Profit % = [(SP − CP) ÷ CP] × 100

Calculations:

⇒ Let the Cost Price (CP) of the article be 100.

⇒ Selling Price (SP₁) = 100 + 44% of 100 = 144

⇒ Equivalent discount of 10% and 20% = 10 + 20 − (10 × 20) ÷ 100 = 28%

⇒ SP₁ = MP × (100 − 28) ÷ 100

⇒ 144 = MP × 0.72

⇒ Marked Price (MP) = 144 ÷ 0.72 = 200

⇒ When the new discount is 15%, the new Selling Price (SP₂) is:

⇒ SP₂ = MP × (100 − 15) ÷ 100

⇒ SP₂ = 200 × 0.85 = 170

⇒ Net Profit = SP₂ − CP = 170 − 100 = 70

⇒ Net Profit % = (70 ÷ 100) × 100 = 70%

∴ The correct answer is 70%.

Additional Information

Successive Discounts

When two or more discounts are applied one after the other on the Marked Price. The equivalent single discount of two successive discounts D₁% and D₂% is calculated as (D₁ + D₂ − (D₁ × D₂) ÷ 100)%.

Marked Price (MP)

The price explicitly tagged on an article before any discount is applied. Discount is always calculated on the MP. General relation: MP = (SP × 100) ÷ (100 − Discount%).

Profit Percentage

Profit is the net gain over the original cost and is always calculated on the Cost Price (CP) unless specifically stated otherwise. Formula: Profit % = [(SP − CP) ÷ CP] × 100.

Given:

$\frac{\sin 30^{\circ} \sin 40^{\circ} \sin 50^{\circ} \sin 60^{\circ}}{\cos 30^{\circ} \cos 40^{\circ} \cos 50^{\circ} \cos 60^{\circ}}$

Concept used:

Sin α = Cos (90° - α)

Calculation:

$\frac{\sin 30^{\circ} \sin 40^{\circ} \sin 50^{\circ} \sin 60^{\circ}}{\cos 30^{\circ} \cos 40^{\circ} \cos 50^{\circ} \cos 60^{\circ}}$

⇒ $\frac{\cos (90 - 30)^{\circ} \cos (90 - 40)^{\circ} \cos (90 - 50)^{\circ} \cos (90 - 60)^{\circ}}{\cos 30^{\circ} \cos 40^{\circ} \cos 50^{\circ} \cos 60^{\circ}}$

⇒ $\frac{\cos 60^{\circ} \cos 50^{\circ} \cos 40^{\circ} \cos 30^{\circ}}{\cos 30^{\circ} \cos 40^{\circ} \cos 50^{\circ} \cos 60^{\circ}}$

⇒ 1

∴ The required value is 1.

Shortcut Trick

Product of two numbers = HCF × LCM

384 = HCF × 48

HCF = 384 ÷ 48 = 8

Ratio of HCF to LCM = 8 : 48 = 1 : 6

∴ The correct answer is 1 : 6.

Alternate Method

Given:

LCM of the two numbers = 48

Product of the two numbers = 384

Formula Used:

Product of two numbers = HCF × LCM

HCF ? → 8

×

LCM 48

=

Product 384

HCF

8 → 1 part

LCM

48 → 6 parts

Ratio HCF : LCM = 1 : 6

Calculations:

⇒ HCF × LCM = Product

⇒ HCF × 48 = 384

⇒ HCF = 384 ÷ 48

⇒ HCF = 8

⇒ Required Ratio = HCF : LCM

⇒ Required Ratio = 8 : 48

⇒ Dividing both sides by 8, we get 1 : 6

∴ The correct answer is 1 : 6.

Additional Information

Product of Two Numbers Rule

For any two positive integers a and b, their product is exactly equal to the product of their HCF and LCM. Formula: a × b = HCF(a, b) × LCM(a, b).

HCF as a Factor of LCM

The Highest Common Factor (HCF) of any set of given numbers is always a strict factor of their Least Common Multiple (LCM). For example, the LCM 48 is perfectly divisible by the HCF 8.

Co-prime Numbers

Two numbers are defined as co-prime if their HCF is 1. Consequently, the LCM of two co-prime numbers is always equal to their exact product.

Shortcut Trick

Total Successive Percentage Increase = [ (Initial Multiplier) − 1 ] × 100.

Successive Multiplier = (110 ÷ 100) × (105 ÷ 100) × (115 ÷ 100) = 1.1 × 1.05 × 1.15.

Product = 1.155 × 1.15 = 1.32825.

Percentage Increase = (1.32825 − 1) × 100 = 32.825%.

Converting to fraction: 32.825 = 32 + 825 ÷ 1000 = 32 + 33 ÷ 40 = 32 33/40 %.

∴ The correct answer is 32 33/40 %.

Alternate Method

Given → Successive increases of 10%, 5%, and 15%. Formulas: Net percentage for two increases a and b = (a + b + ab ÷ 100)%.

⇒ Combine first two: 10 + 5 + (10 × 5 ÷ 100) = 15 + 0.5 = 15.5%. ⇒ Combine result with third: 15.5 + 15 + (15.5 × 15 ÷ 100). ⇒ 30.5 + (232.5 ÷ 100) = 30.5 + 2.325 = 32.825%. ⇒ Total Increase = 32825 ÷ 1000 = 1313 ÷ 40 = 32 33/40 %.

∴ The correct answer is 32 33/40 %.

Additional Information

Successive Percentage Change

When a value is increased by x% and then y%, the total change is not simply x + y, but includes the interest on the first increase.

Fractional Conversion

To convert a decimal percentage like 0.825% to a fraction, divide by 1000 and simplify: 825/1000 = 165/200 = 33/40.

Given:

Areas of similar triangles ΔABC and ΔDEF are x2 cm2 and y2 cm2 respectively

EF = a cm

Concept used:

If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.

Calculation:

As ΔABC ∼ ΔDEF

So, (BC/EF)² = Area of ΔABC/Area of ΔDEF

⇒ BC²/a2 = x²/y²

⇒ BC/a = x/y

⇒ BC = ax/y

∴ BC (in cm) is $\frac{a x}{y}$.

Given:

The average of the marks of 25 students in a class, in an examination was calculated to be 19.

Wrong marks are 18 and 19

Correct marks are 14 and 15

Concept used:

Average = Sum of elements/Number of elements

Calculation:

Total marks of 25 students with wrong numbers = 25 × 19

⇒ 475

Correct total = 475 - (18 + 19) + 14 + 15

⇒ 475 - 37 + 29

⇒ 467

So, new average = 467/25

⇒ 18.68

∴ The new actual average mark of the class is 18.68.

Given:

x9 × x5 × x-4 × x0 × x-6

Concept used:

x^a × x^b = x^{(a + b)}

xa ÷ xb = x(a - b)

Calculation:

x9 × x5 × x-4 × x0 × x-6

⇒ x9 × x5 × 1/x⁴ × 1 × 1/x6

⇒ x9 × x × 1/x6

⇒ x9 × 1/x5

⇒ x4

∴ The required answer is x4.

Given:

(sin 30° cos 60° - cos 30° sin 60°)

Concept used:

Calculation:

(sin 30° cos 60° - cos 30° sin 60°)

⇒ (1/2 × 1/2 - √3/2 × √3/2)

⇒ (1/4 - 3/4)

⇒ - 2/4

⇒ - 1/2 = -sin 30°

∴ The required answer is -sin 30°.

Formula Used:

For 2 numbers a,b,

Mean proportion = √ab

Third proportion = b²/a

Calculation:

Mean proportion of 1.6 and 3.6 = √(1.6 × 3.6)

⇒ 2.4

The third proportion of 5 and 8,

64/5

Required ratio = (2.4 : 64/5) = 12 : 64

⇒ 3 : 16

∴ The required answer is 3 : 16.

Given:

The difference between the cost price and selling price of a pair of shoes is Rs. 1,200

Profit % = 15%

Concept used:

Selling price = Cost price × (100 + profit)%

Calculation:

Let the cost price of the pair of shoes be 100a

So, selling price = 100a × 115%

⇒ 115a

According to the question,

115a - 100a = 1200

⇒ 15a = 1200

⇒ a = 80

So, selling price = 115 × 80

⇒ 9200

∴ The selling price is Rs. 9200.

Given:

Rate = 25%

Time = 6

Formula used:

SI =(PRT)/100

Here,

P = Sum

R = rate

T = time

Calculation:

Let the amount lent be Rs. y

According to the question,

360 + y = (y × 6 × 25)/100

⇒ 360 + y = 1.5y

⇒ 360 = 1.5y - y

⇒ 360 = 0.5y

⇒ y = 720

∴ The sum lent is Rs. 720.

Shortcut Trick

For an equilateral triangle with side a, the circumradius (R) is given by the formula R = a / √3.

Given a = 12 cm.

⇒ R = 12 / √3

⇒ R = (4 × 3) / √3 = 4√3 cm.

∴ The correct answer is 4√3 cm.

Alternate Method

Given:

Side of the equilateral triangle (a) = 12 cm.

Formula Used:

Circumradius (R) = a / √3

Calculations:

⇒ Circumradius (R) = 12 / √3

⇒ Multiply numerator and denominator by √3:

⇒ R = (12 × √3) / (√3 × √3)

⇒ R = 12√3 / 3

⇒ R = 4√3 cm

∴ The correct answer is 4√3 cm.

Additional Information

Inradius of Equilateral Triangle

The radius of the incircle (r) is half of the circumradius: r = a / (2√3).

Height of Equilateral Triangle

The altitude or height (h) is given by h = (√3 / 2) × a, and the circumradius is 2/3 of this height.

Area of Equilateral Triangle

The area is calculated using the formula: Area = (√3 / 4) × a².

Calculation:

Total cooler sold by shop E = 4000 × (1/10)

⇒ 400

Selling price of 400 coolers = 400 × 8000

⇒ 3200000

Total ACs sold by shop E = 4000 × (5/10)

⇒ 2000

Selling price of 2000 ACs = 2000 × 26500

⇒ 53000000

Total Fans sold by shop E = 4000 × (4/10)

⇒ 1600

Selling price of 1600 Fans = 1600 × 12200

⇒ 19520000

Now,

Required % = [3200000/(3200000 + 53000000 + 19520000)] × 100

⇒ [3200000/(75720000)] × 100

⇒ 4.226 ≈ 4.23%

∴ The required answer is 4.23%.

Calculation:

Overall percentage obtained by A = (92 + 90 + 90 + 80)/400 × 100% = 88%

Overall percentage obtained by B = (90 + 80 + 85 + 85)/400 × 100% = 85%

Overall percentage obtained by C = (80 + 80 + 65 + 70)/400 × 100% = 73.75%

Overall percentage obtained by D = (85 + 80 + 82 + 75)/400 × 100% = 80.5%

Overall percentage obtained by E = (80 + 75 + 75 + 85)/400 × 100% = 78.75%

Overall percentage obtained by F = (90 + 90 + 90 + 85)/400 × 100% = 88.75%

Here, A, B, D, and F have obtained more than 80% overall percentage.

∴ The number of students whose overall percentage obtained is 80% and above is 4.

Calculation:

Now, the ratio of number of person participating in a survey from state S3 to the number of person participating in a survey from state S4

⇒ 400 : 500 = 4 : 5

∴ The ratio of number of person participating in a survey from state S3 to the number of person participating in a survey from state S4 is 4 : 5.

Calculation:

8127

⇒ 8000 + 120 + 7

Here, both 8000 and 120 are divisible by 8.

Now, the remainder when 8127 is divided by 8 is 7

∴ The remainder when 8127 is divided by 8 is 7.

Shortcut Trick

Total work = LCM(10, 20, 40) = 40 units.

Daily efficiency: A = 4, B = 2, C = 1.

Work in one 3-day cycle = A + A + (A + B + C) = 4 + 4 + 7 = 15 units.

Work done in 6 days (2 cycles) = 30 units, leaving 10 units of remaining work.

Next 2 days, A completes 8 units (4 × 2). The remaining 2 units are done by A, B, and C in 2/7 days.

∴ The correct answer is 8 ²/₇ days.

Alternate Method

Given:

Time taken by A = 10 days

Time taken by B = 20 days

Time taken by C = 40 days

Formula Used:

Total Work = LCM of given days

Efficiency = Total Work ÷ Days

Calculations:

⇒ Work done on Day 1 (by A) = 4 units

⇒ Work done on Day 2 (by A) = 4 units

⇒ Work done on Day 3 (by A + B + C) = 4 + 2 + 1 = 7 units

⇒ Work done in one complete 3-day cycle = 4 + 4 + 7 = 15 units

⇒ Number of full cycles = 40 ÷ 15 = 2 cycles (with remainder)

⇒ Work done in 2 cycles (6 days) = 15 × 2 = 30 units

⇒ Remaining work = 40 − 30 = 10 units

⇒ On Day 7, A completes 4 units → Remaining work = 6 units

⇒ On Day 8, A completes 4 units → Remaining work = 2 units

⇒ On Day 9, A, B, and C work together with a combined efficiency of 7 units/day

⇒ Time taken to complete the last 2 units = 2 ÷ 7 days

⇒ Total time taken = 6 + 1 + 1 + 2/7 = 8 ²/₇ days

∴ The correct answer is 8 ²/₇ days.

Additional Information

LCM Method for Time & Work

Total work is assumed as the Least Common Multiple (LCM) of the time taken by each individual. This guarantees that calculating efficiency always results in simple integer values.

Alternate Day Work Concept

When workers operate in a repeated pattern, first calculate the combined work done in one complete cycle. Multiply the cycle length to get as close to the total work as possible before resolving the final days individually.

Work & Wages

Wages are strictly distributed in proportion to the total physical work completed by each person. If all members work for the same total duration, wages are simply split in the ratio of their efficiencies.