June 20, 2022

Time and Work is one of the most familiar quantitative aptitude topics which is asked in the CLAT examination. This is one of those topics which candidates are familiar with even before they start their CLAT exam preparation.

The concept of time and work remains the same, however, the type of questions asked may have a portion which varies in every question. Mostly, in CLAT (Common Law Admission Test) examination 1-2 word problems are asked from this topic but candidates must also keep themselves prepared to have questions in data sufficiency and data interpretation to be picked up from time and work.

Before we start understanding the questions and important formulas, it is crucial that a candidate is well aware of the concept and the types of questions which may be asked in the CLAT examination.

Time and work deals with the time taken by an individual or a group of individuals to complete a piece of work and the efficiency of the work done by each of them.

Work to be done is generally considered as one unit, it may be digging a bench, constructing or painting a wall, filling up or emptying a tank, reservoir or a cistern.

Download FREE Study Material for CLAT 2023 by LegalEdge

Now, below you will get to know the important information that will help you to solve Time and Work related questions.

- It takes (T) time to complete a certain amount of work (W). The number of units of work done per unit time is called the rate of work (R).

**Thus, Work (W) = Time (T) x Rate of Work (R).**

- Rate of work and time are inversely proportional to each other.

**Thus, R = 1 / T.**

- If A can do a piece of work in ‘n’ days, then Work done by A in 1 day = 1 / n

For example, If a person can do some work in 12 days then it means he does 1 / 12th of the work in one day.

- If A’s 1 day work = 1 / n, then A can finish the whole work in ‘n’ days.

For example, If a person’s one day of work is 1 / 10, then he can finish the whole work in 10 days.

- If A is twice as good as a workman as B, then the ratio of work done by A and B = 2 : 1 ; And the ration of time taken by A and B = 1 : 2.

Important Maths Formulas for CLAT 2023

For example, If a man works two times as fast as a woman does, then on completion of the work 2 parts of the work has been done by the man and 1 part by the woman. Also, if they work individually then the woman takes 10 days to complete the work and the man takes 5 days to complete the work.

- If two persons A and B can individually do some work in ‘a’ and ‘b’ days respectively, then A and B together can complete the same work in ab / a + b days. {1 / 1 / a + 1 / b = ab / a + b}
- If two persons A and B together can complete the same work in ‘a’ days and A (or B) can individually do same work in b days, then B (or A) can complete the work in ab / b - a days.

Below mentioned are the type of questions which may be asked in the Common Law Admission Test (CLAT) from the time and work topic: -

- To find the efficiency of a person
- To find the time taken by an individual to do a piece of work
- To find the time taken by a group of individuals to complete a piece of work
- Work done by an individual in a certain time duration
- Work done by a group of individuals in a certain time duration

In this article, you will get all the types of questions that are asked in the time and work topic in the common law admission test (CLAT).

How to Attempt Quant Section in CLAT 2023

**Question 1: **A can do a piece of work in 10 days and B can do the same work in 30 days. In how many days can the work be completed if A and B work together?

(1). 4 5 / 2

(2). 7 1 / 2

(3). 6 9 / 5

(4). 2 3 / 5

(5). None of these

**Answer: (2) 7 1 / 2**

**Explanation:**

To Given: A’s 1 day’s work = 1 / 10

B’s 1 day work = 1 / 30

To Find: How many days can the work be completed if A and B work together?

Solution:

A’s 1 day’s work = 1 / 10

B’s 1 day work = 1 / 30

Therefore,

(A + B)’s 1 day’s work = 1 / 10 + 1 / 30

(A + B)’s 1 day’s work = 2 / 15

Hence, A and B together can do the work in 15 / 2 days, i.e. **7 1 / 2 days.**

**Question 2: **A and B together can do a piece of work in 9 days. ‘A’ Alone can complete the work in 12 days. How long will B alone take to complete the job?

(1). 30 days

(2). 50 days

(3). 60 days

(4). 36 days

(5). 20 days

**Answer: (4) 36 days**

**Explanation: **

To Given: (A + B)’s 1 day’s work = 1 / 9

A’s Alone 1 day’s work = 1 / 12

To Find: B’s Alone 1 day’s work?

Solution:

(A + B)’s 1 day’s work = 1 / 9

A’s Alone 1 day’s work = 1 / 12

Therefore,

B’s Alone 1 day’s work = 1 / 9 - 1/ 12

B’s Alone 1 day’s work = 1 / 36.

So, B alone can do the work in 36 days.

**Question 3: **A can do work in 25 days. When he had worked for 15 days, B replaced him. If he completes the remaining work in 10 days, in how many days can B alone finish the work?

(1). 20 days

(2). 10 days

(3). 30 days

(4). 40 days

(5). None of these

**Answer: (5) None of these**

**Explanation:**

To given: A’s 1 day’s work = 1 / 25

A’s 15 day’s work = 15 / 25

To find: In how many days can B alone finish the work?

Solution:

A’s 1 day’s work = 1 / 25

A’s 15 day’s work = 15 / 25

A’s 15 day’s work = 3 / 5

Work remaining = (1 - 3 / 5) = 2 / 5 which is done by B in 10 days.

Therefore,

**B can do the work alone in (5 / 2 x 10) = 25 days**

**Question 4: **A is thrice as good a workman as B and is therefore able to finish a piece of work in 30 days less than B. Find the time in which they can do it working together.

(1). 11 1 / 4

(2). 5 2 / 3

(3). 6 2 / 3

(4). 20 4 / 2

(5). None of these.

**Answer: (1). 11 1 / 4**

**Explanation:**

To given: A is thrice as good as workman as B

To find: the time in which they can do it working together?

Solution:

The ratio of work done by A and B in the same time = 3 : 1

Ratio of time taken by A and B = 1 : 3

Let B takes π₯ days to finish a work.

Then,

A takes (π₯ - 30) days to finish it.

Therefore,

⇒ π₯ - 30 / π₯ = 1 / 3

⇒ 3π₯ - 90 = π₯

⇒ π₯ = 45 days

Thus, A and B can finish the work in 15 days and 45 days, respectively.

Now, (A + B)’s 1 day’s work = 1 / 15 + 1 / 45 = 4 / 45.

**So, both together can finish the work in 45 / 4 days = 11 1 / 4 days.**

Attempt Short Quiz on Time and Work for CLAT 2023

**Question 5: **1 woman or 2 men or 3 boys can do a piece of work in 55 days, then the same piece of work will be done by 1 man, 1 woman and 1 boy in how many days?

(1). 18 days

(2). 30 days

(3). 32 days

(4). 16 days

(5). None of these

**Answer: (2) 30 days**

**Explanation:**

To given: 1 woman = 2 man = 3 boys

To find: the same piece of work will be done by 1 man, 1 woman and 1 boy in how many days?

Solution:

1 woman = 2 man = 3 boys

⇒ 1 boy = 2 / 3 man.

⇒ 1 man + 1 woman + 1 boy = 1 man + 2 men + 2 / 3 men

⇒ (1 + 2 + 2 / 3) = 11 / 3 men.

If 2 men can do work in 55 days.

Then,

⇒ 11 / 3 men will do the same work in = 2 x 55 x 3 / 11 = 30 days.

**So, 1 man, 1 woman, and 1 boy will completer the same piece of work in 30 days**

**Question 6: **If 5 men and 2 boys are working together, can do three times as much work per hour as a man and a boy together. The ratio of the work done by a man and that of a boy for a given time is

(1). 1 : 2

(2). 2 : 1

(3). 1 : 3

(4). 3 : 1

(5). None of these

**Answer: (1) 1 : 2**

**Explanation:**

To given: 5 men and 2 boys are working together, and can do three times as much work per hour as a man and a boy together.

To find: ratio of the work done by a man and that of a boy for a given time

Solution:

⇒ 5 men + 2 boy = 3 (1 man + 1 boy)

⇒ 5 men + 2 boy = 3 men + 3 boy

⇒ 2 men = 1 boy

Therefore,

The required ratio of work done by a man and a boy = 1 : 2

**Question 7: **If 2 men and 3 boys can do a piece of work in 16 days and 3 men and 2 boys can do it in 14 days, how long will 5 men and 4 boys take to do it?

(1). 6 days

(2). 8 days

(3). 9 days

(4). 10 days

(5). None of these

**Answer: (2) 8 days**

**Explanation:**

To given: 2 men and 3 boys can do a piece of work in 16 days and 3 men and 2 boys can do it in 14 days.

To find: how long will 5 men and 4 boys take to do it?

Solution:

⇒ 2 men + 3 boys = 16 days

⇒ 2 x 16 men + 3 x 16 boys = 1 day

⇒ 32 men + 48 boys = 1 day …………….. Equation (1)

And

⇒ 3 men + 2 boy = 14 days

⇒ 42 men + 28 boys = 1 day ………….. Equation (2)

On solving Equation (2), we get

⇒ 1 men = 2 boys

⇒ 2 men + 3 boys = 4 boys + 3 boys

⇒ 2 men + 3 boys = 7 boys

And

⇒ 5 men + 4 boys = 10 boys + 4 boys

⇒ 5 men + 4 boys = 14 boys

Now, 7 boys take = 16 days

Therefore,

⇒ 14 boys take = 16 x 7 / 14

** ⇒ 14 boys take = 8 days**

**Question 8: **A and B complete a piece of work in 5 days working together. If A had worked twice the work would have been completed in 4 days. In how many days can A alone complete the work?

(1). 20 days

(2). 18 days

(3). 24 days

(4). 15 days

(5). None of these

**Answer: (1). 20 days**

**Explanation:**

To given: A and B complete a piece of work in 5 days working together.

To find: In how many days can A alone complete the work?

Solution:

Let A do the work in ‘a’ days.

A’s 1 day’s work = 1 / a

Let B do the work in ‘b’ days.

B’s 1 day’s work = 1 / b

Now,

⇒ 1 / a + 1 / b = 1 / 5 …………… Equation (1)

⇒ 2 / a + 1 / b = 1 / 4 ……………. Equation (2)

By solving Equation (1) and Equation (2), we get

⇒ a = 20 days.

**Hence, A alone will complete the work in 20 days.**

**Question 9: **If I must hire 6 men and 8 boys for 6 days to do the same piece of work as 8 men and 15 boys could do in 4 days, compare the efficiency ratio of the men and the boys.

(1). 1 : 2

(2). 1 : 3

(3). 1 : 4

(4). 1 : 5

(5). None of these

**Answer: (5). None of these**

**Explanation:**

To given: 6 men + 8 boys can do a piece of work in 6 days

8 men + 15 boys can do a piece of work in 4 days

To find: compare the efficiency ratio of the men and the boys.

Solution:

⇒ (6 men + 8 boys) can do a piece of work in 6 days

⇒ (8 men + 15 boys) can do a piece of work in 4 days

⇒ (6 men + 8 boys) can do a piece of work in 6 days

⇒ (36 men + 48 boys) can do the work in 1 day

⇒ (8 men + 15 boys) can do a piece of work in 4 days

⇒ (32 men + 60 boys) can do the work in 1 day

⇒ 36 men + 48 boys = 32 men + 60 boys

⇒ 36 men - 32 men = 60 boys - 48 boys

⇒ 4 men = 12 boys

⇒ men = 3 boys

**Therefore, the ratio of efficiency of men and boys = 3 : 1.**

**Question 10: **3 men or 5 women can do work in 6 days. How long will 6 men and 5 women take to finish the work?

(1). 2.5 days

(2). 2 days

(3). 3 days

(4). 3.5 days

(5). None of these

**Answer: (2). 2 days**

**Explanation:**

To given: 3 men or 5 women can do work in 6 days

To find: How long will 6 men and 5 women take to finish the work?

Solution:

3 men = 5 women

Or

⇒ 3 x 5 x 6 / (3 x 5 + 6 x 5)

⇒ 3 x 5 x 6 / 45 = 2

⇒ 1 man = 5 / 3 women

⇒ 6 men + 5 women = (6 x 5 / 3 + 5)

⇒ women = 15 women.

Now, if 5 women can do work in 6 days.

⇒ 15 women can do it in (5 x 6 / 15) days = 2 days

**Hence, 6 men and 5 women will take 2 days to finish the work.**

** Question 11: **4 men can do a piece of work in 10 days, 2 women can do it in 15 days and 5 children can do it in 12 days. In how many days can 8 men, 5 women and 15 children together complete the piece of work?

(1). 2 days

(2). 3 days

(3). 4 days

(4). 5 days

(5). None of these

**Answer: (5) None of these**

**Explanation:**

To given: 4 men’s 1 day’s work = 1 / 10.

1 man’s 1 day’s work = 1 / 40.

2 women’s 1 day’s work = 1 / 15.

1 woman’s 1 day’s work = 1 / 30.

5 children’s 1 day’s work = 1 / 12.

1 child’s 1 day’s work = 1 / 60.

To find: In how many days can 8 men, 5 women and 15 children together complete the piece of work?

Solution:

⇒ 4 men’s 1 day’s work = 1 / 10.

⇒ 1 man’s 1 day’s work = 1 / 40.

⇒ 2 women’s 1 day’s work = 1 / 15.

⇒ 1 woman’s 1 day’s work = 1 / 30.

⇒ 5 children’s 1 day’s work = 1 / 12.

⇒ 1 child’s 1 day’s work = 1 / 60.

Now,

⇒ (8 men + 5 women + 15 children)’s 1 day’s work = 8 / 40 + 5 / 30 + 15 / 60

⇒ (8 men + 5 women + 15 children)’s 1 day’s work = 1 / 5 + 1 / 6 + 1 / 4

⇒ (8 men + 5 women + 15 children)’s 1 day’s work = 37 / 60.

**So, they can finish the work in 60 / 37 days.**

**Question 12: **3 men can do a piece of work in 12 days, 5 women in 8 days and 20 children in 3 days. In how many days can a man, a woman, and a child work together to complete the piece of work?

(1). 12 days

(2). 13 days

(3). 14 days

(4). 15 days

(5). None of these

**Answer: (5). None of these**

**Explanation:**

To given: 3 men can do a piece of work in 12 days

5 women can do a piece of work in 8 days.

20 children can do a piece of work in 3 days.

To find: In how many days can a man, a woman, and a child work together to complete the piece of work?

Solution:

⇒ 3 men can do a piece of work in 12 days

⇒ 1 man will do the same piece of work in 36 days.

⇒ 5 women can do a piece of work in 8 days.

⇒ 1 woman will do the same piece of work in 40 days

⇒ 20 children can do a piece of work in 3 days.

⇒ 1 child will do the same piece of work in 60 days.

Now,

⇒ (1 man + 1 woman + 1 child)’s 1 day’s work = 1 / 36 + 1 / 40 + 1 / 60

⇒ (1 man + 1 woman + 1 child)’s 1 day’s work = 5 / 72.

**So, the work is complete in 72 / 5 days = 14 2 / 5 days**

**Question 13: **A certain number of men can complete a piece of work in 40 days. If there were 8 men more the work could be finished in 10 days less. How many men were there afterwards?

(1). 32 men

(2). 28 men

(3). 24 men

(4). 15 men

(5). None of these

**Answer: (1). 32 men**

**Explanation:**

Let the number of men be π₯.

π₯ men can do a work in 40 days.

(π₯ + 8) men can do the same work in (40 - 10) = 30 days.

⇒ π₯ x 40 = 30 (π₯ + 8)

⇒ 40π₯ = 30π₯ + 240

⇒ 40π₯ - 30π₯ = 240

⇒ 10π₯ = 240

⇒ π₯ = 24.

Therefore,

**The number of men afterwards = 24 + 8 = 32 men**

**Question 14: **If A can d0 ¼ of the work in 4 days and B can do β
of the work in 3 days, how much will A get if both work together and are paid Rs. 4,500 in all?

(1). Rs. 1,800

(2). Rs. 2,400

(3). Rs. 2,700

(4). Rs. 2,900

(5). None of these

**Answer: (3). Rs. 2,700**

**Explanation:**

Whole work is done by A in (4 x 4) days = 16 days

Whole work is done by Bin (8 x 3) days = 24 days.

A’s wages : B’s wages

⇒ A’s 1 day’s work : B’s 1 day's work

⇒ 1/16 : 1/24

⇒ 3 : 2

Therefore,

⇒ A’s sheet = (β x 4,500)

**⇒ A’s sheet = Rs. 2,700.**

**Question 15: **6 men can complete a piece of work in 12 days. 8 women can do the same piece of work in 18 days whereas 18 children can complete it in 10 days. 4 men, 12 women and 20 children work together for 2 days. If only men were to complete the remaining work in 1 day, how many men would be required totally?

(1). 36 men

(2). 24 men

(3). 18 men

(4). Cannot be determined

(5). None of these

**Answer: (1). 36 men**

**Explanation:**

⇒ (6 x 12) men = (8 x 18) women = (18 x 10) children.

⇒ 2 men = 4 women = 5 children

Now, 4 men + 12 women + 20 children = 4 men + 6 men + 8 men = 18 men

⇒ 6 men’s 1 day’s work = 1/12

⇒ 18 men’s 1 day’s work = 1/12 x 18/6 = ¼

⇒ 18 men’s 2 day’s work = ¼ x 2

⇒ 18 men’s 2 day’s work = ½

Therefore,

The remaining work = 1 - ½

⇒ remaining work = ½

Remaining work can be complete by 18 men in 2 days

**Therefore, to complete in 1 day, men required = 2 x 18 = 36 men**

Frequently Asked Questions

How can I improve my accuracy in the CLAT exam?

You can easily improve your speed and accuracy in the CLAT Exam by solving as many sample papers as possible. Practicing mock tests would definitely improve your time management skills and problem-solving techniques. So, it is advisable to solve mock tests on a daily basis.

Do I need to take specific coaching for CLAT Maths?

It solely depends on you whether you need to take CLAT coaching or not. If your fundamentals are strong, then it is easy to crack the exam just by solving previous year sample papers and Mock tests. However, if you want to improve your fundamentals then opting for coaching is beneficial.

What are the important topics of CLAT Maths Syllabus?

The important topics of CLAT Maths Syllabus are Profit & Loss, InterestNumber system, Surds & Indices, Ratio & Proportion, Percentage, HCF & LCM, and Interest.

What is the Difficulty level of Math Section in CLAT?

Based on the previous year's CLAT Exam Analysis, the Math Section's difficulty level was easy to moderate.

Is 1 month preparation enough for CLAT Maths Preparation?

Yes. With a proper preparation strategy, it is easy to prepare for the CLAT Mathematics section.

Updated On : June 20, 2022

Time and Work is one of the most familiar quantitative aptitude topics which is asked in the CLAT examination. This is one of those topics which candidates are familiar with even before they start their CLAT exam preparation.

The concept of time and work remains the same, however, the type of questions asked may have a portion which varies in every question. Mostly, in CLAT (Common Law Admission Test) examination 1-2 word problems are asked from this topic but candidates must also keep themselves prepared to have questions in data sufficiency and data interpretation to be picked up from time and work.

Before we start understanding the questions and important formulas, it is crucial that a candidate is well aware of the concept and the types of questions which may be asked in the CLAT examination.

Time and work deals with the time taken by an individual or a group of individuals to complete a piece of work and the efficiency of the work done by each of them.

Work to be done is generally considered as one unit, it may be digging a bench, constructing or painting a wall, filling up or emptying a tank, reservoir or a cistern.

Download FREE Study Material for CLAT 2023 by LegalEdge

Now, below you will get to know the important information that will help you to solve Time and Work related questions.

- It takes (T) time to complete a certain amount of work (W). The number of units of work done per unit time is called the rate of work (R).

**Thus, Work (W) = Time (T) x Rate of Work (R).**

- Rate of work and time are inversely proportional to each other.

**Thus, R = 1 / T.**

- If A can do a piece of work in ‘n’ days, then Work done by A in 1 day = 1 / n

For example, If a person can do some work in 12 days then it means he does 1 / 12th of the work in one day.

- If A’s 1 day work = 1 / n, then A can finish the whole work in ‘n’ days.

For example, If a person’s one day of work is 1 / 10, then he can finish the whole work in 10 days.

- If A is twice as good as a workman as B, then the ratio of work done by A and B = 2 : 1 ; And the ration of time taken by A and B = 1 : 2.

Important Maths Formulas for CLAT 2023

For example, If a man works two times as fast as a woman does, then on completion of the work 2 parts of the work has been done by the man and 1 part by the woman. Also, if they work individually then the woman takes 10 days to complete the work and the man takes 5 days to complete the work.

- If two persons A and B can individually do some work in ‘a’ and ‘b’ days respectively, then A and B together can complete the same work in ab / a + b days. {1 / 1 / a + 1 / b = ab / a + b}
- If two persons A and B together can complete the same work in ‘a’ days and A (or B) can individually do same work in b days, then B (or A) can complete the work in ab / b - a days.

Below mentioned are the type of questions which may be asked in the Common Law Admission Test (CLAT) from the time and work topic: -

- To find the efficiency of a person
- To find the time taken by an individual to do a piece of work
- To find the time taken by a group of individuals to complete a piece of work
- Work done by an individual in a certain time duration
- Work done by a group of individuals in a certain time duration

In this article, you will get all the types of questions that are asked in the time and work topic in the common law admission test (CLAT).

How to Attempt Quant Section in CLAT 2023

**Question 1: **A can do a piece of work in 10 days and B can do the same work in 30 days. In how many days can the work be completed if A and B work together?

(1). 4 5 / 2

(2). 7 1 / 2

(3). 6 9 / 5

(4). 2 3 / 5

(5). None of these

**Answer: (2) 7 1 / 2**

**Explanation:**

To Given: A’s 1 day’s work = 1 / 10

B’s 1 day work = 1 / 30

To Find: How many days can the work be completed if A and B work together?

Solution:

A’s 1 day’s work = 1 / 10

B’s 1 day work = 1 / 30

Therefore,

(A + B)’s 1 day’s work = 1 / 10 + 1 / 30

(A + B)’s 1 day’s work = 2 / 15

Hence, A and B together can do the work in 15 / 2 days, i.e. **7 1 / 2 days.**

**Question 2: **A and B together can do a piece of work in 9 days. ‘A’ Alone can complete the work in 12 days. How long will B alone take to complete the job?

(1). 30 days

(2). 50 days

(3). 60 days

(4). 36 days

(5). 20 days

**Answer: (4) 36 days**

**Explanation: **

To Given: (A + B)’s 1 day’s work = 1 / 9

A’s Alone 1 day’s work = 1 / 12

To Find: B’s Alone 1 day’s work?

Solution:

(A + B)’s 1 day’s work = 1 / 9

A’s Alone 1 day’s work = 1 / 12

Therefore,

B’s Alone 1 day’s work = 1 / 9 - 1/ 12

B’s Alone 1 day’s work = 1 / 36.

So, B alone can do the work in 36 days.

**Question 3: **A can do work in 25 days. When he had worked for 15 days, B replaced him. If he completes the remaining work in 10 days, in how many days can B alone finish the work?

(1). 20 days

(2). 10 days

(3). 30 days

(4). 40 days

(5). None of these

**Answer: (5) None of these**

**Explanation:**

To given: A’s 1 day’s work = 1 / 25

A’s 15 day’s work = 15 / 25

To find: In how many days can B alone finish the work?

Solution:

A’s 1 day’s work = 1 / 25

A’s 15 day’s work = 15 / 25

A’s 15 day’s work = 3 / 5

Work remaining = (1 - 3 / 5) = 2 / 5 which is done by B in 10 days.

Therefore,

**B can do the work alone in (5 / 2 x 10) = 25 days**

**Question 4: **A is thrice as good a workman as B and is therefore able to finish a piece of work in 30 days less than B. Find the time in which they can do it working together.

(1). 11 1 / 4

(2). 5 2 / 3

(3). 6 2 / 3

(4). 20 4 / 2

(5). None of these.

**Answer: (1). 11 1 / 4**

**Explanation:**

To given: A is thrice as good as workman as B

To find: the time in which they can do it working together?

Solution:

The ratio of work done by A and B in the same time = 3 : 1

Ratio of time taken by A and B = 1 : 3

Let B takes π₯ days to finish a work.

Then,

A takes (π₯ - 30) days to finish it.

Therefore,

⇒ π₯ - 30 / π₯ = 1 / 3

⇒ 3π₯ - 90 = π₯

⇒ π₯ = 45 days

Thus, A and B can finish the work in 15 days and 45 days, respectively.

Now, (A + B)’s 1 day’s work = 1 / 15 + 1 / 45 = 4 / 45.

**So, both together can finish the work in 45 / 4 days = 11 1 / 4 days.**

Attempt Short Quiz on Time and Work for CLAT 2023

**Question 5: **1 woman or 2 men or 3 boys can do a piece of work in 55 days, then the same piece of work will be done by 1 man, 1 woman and 1 boy in how many days?

(1). 18 days

(2). 30 days

(3). 32 days

(4). 16 days

(5). None of these

**Answer: (2) 30 days**

**Explanation:**

To given: 1 woman = 2 man = 3 boys

To find: the same piece of work will be done by 1 man, 1 woman and 1 boy in how many days?

Solution:

1 woman = 2 man = 3 boys

⇒ 1 boy = 2 / 3 man.

⇒ 1 man + 1 woman + 1 boy = 1 man + 2 men + 2 / 3 men

⇒ (1 + 2 + 2 / 3) = 11 / 3 men.

If 2 men can do work in 55 days.

Then,

⇒ 11 / 3 men will do the same work in = 2 x 55 x 3 / 11 = 30 days.

**So, 1 man, 1 woman, and 1 boy will completer the same piece of work in 30 days**

**Question 6: **If 5 men and 2 boys are working together, can do three times as much work per hour as a man and a boy together. The ratio of the work done by a man and that of a boy for a given time is

(1). 1 : 2

(2). 2 : 1

(3). 1 : 3

(4). 3 : 1

(5). None of these

**Answer: (1) 1 : 2**

**Explanation:**

To given: 5 men and 2 boys are working together, and can do three times as much work per hour as a man and a boy together.

To find: ratio of the work done by a man and that of a boy for a given time

Solution:

⇒ 5 men + 2 boy = 3 (1 man + 1 boy)

⇒ 5 men + 2 boy = 3 men + 3 boy

⇒ 2 men = 1 boy

Therefore,

The required ratio of work done by a man and a boy = 1 : 2

**Question 7: **If 2 men and 3 boys can do a piece of work in 16 days and 3 men and 2 boys can do it in 14 days, how long will 5 men and 4 boys take to do it?

(1). 6 days

(2). 8 days

(3). 9 days

(4). 10 days

(5). None of these

**Answer: (2) 8 days**

**Explanation:**

To given: 2 men and 3 boys can do a piece of work in 16 days and 3 men and 2 boys can do it in 14 days.

To find: how long will 5 men and 4 boys take to do it?

Solution:

⇒ 2 men + 3 boys = 16 days

⇒ 2 x 16 men + 3 x 16 boys = 1 day

⇒ 32 men + 48 boys = 1 day …………….. Equation (1)

And

⇒ 3 men + 2 boy = 14 days

⇒ 42 men + 28 boys = 1 day ………….. Equation (2)

On solving Equation (2), we get

⇒ 1 men = 2 boys

⇒ 2 men + 3 boys = 4 boys + 3 boys

⇒ 2 men + 3 boys = 7 boys

And

⇒ 5 men + 4 boys = 10 boys + 4 boys

⇒ 5 men + 4 boys = 14 boys

Now, 7 boys take = 16 days

Therefore,

⇒ 14 boys take = 16 x 7 / 14

** ⇒ 14 boys take = 8 days**

**Question 8: **A and B complete a piece of work in 5 days working together. If A had worked twice the work would have been completed in 4 days. In how many days can A alone complete the work?

(1). 20 days

(2). 18 days

(3). 24 days

(4). 15 days

(5). None of these

**Answer: (1). 20 days**

**Explanation:**

To given: A and B complete a piece of work in 5 days working together.

To find: In how many days can A alone complete the work?

Solution:

Let A do the work in ‘a’ days.

A’s 1 day’s work = 1 / a

Let B do the work in ‘b’ days.

B’s 1 day’s work = 1 / b

Now,

⇒ 1 / a + 1 / b = 1 / 5 …………… Equation (1)

⇒ 2 / a + 1 / b = 1 / 4 ……………. Equation (2)

By solving Equation (1) and Equation (2), we get

⇒ a = 20 days.

**Hence, A alone will complete the work in 20 days.**

**Question 9: **If I must hire 6 men and 8 boys for 6 days to do the same piece of work as 8 men and 15 boys could do in 4 days, compare the efficiency ratio of the men and the boys.

(1). 1 : 2

(2). 1 : 3

(3). 1 : 4

(4). 1 : 5

(5). None of these

**Answer: (5). None of these**

**Explanation:**

To given: 6 men + 8 boys can do a piece of work in 6 days

8 men + 15 boys can do a piece of work in 4 days

To find: compare the efficiency ratio of the men and the boys.

Solution:

⇒ (6 men + 8 boys) can do a piece of work in 6 days

⇒ (8 men + 15 boys) can do a piece of work in 4 days

⇒ (6 men + 8 boys) can do a piece of work in 6 days

⇒ (36 men + 48 boys) can do the work in 1 day

⇒ (8 men + 15 boys) can do a piece of work in 4 days

⇒ (32 men + 60 boys) can do the work in 1 day

⇒ 36 men + 48 boys = 32 men + 60 boys

⇒ 36 men - 32 men = 60 boys - 48 boys

⇒ 4 men = 12 boys

⇒ men = 3 boys

**Therefore, the ratio of efficiency of men and boys = 3 : 1.**

**Question 10: **3 men or 5 women can do work in 6 days. How long will 6 men and 5 women take to finish the work?

(1). 2.5 days

(2). 2 days

(3). 3 days

(4). 3.5 days

(5). None of these

**Answer: (2). 2 days**

**Explanation:**

To given: 3 men or 5 women can do work in 6 days

To find: How long will 6 men and 5 women take to finish the work?

Solution:

3 men = 5 women

Or

⇒ 3 x 5 x 6 / (3 x 5 + 6 x 5)

⇒ 3 x 5 x 6 / 45 = 2

⇒ 1 man = 5 / 3 women

⇒ 6 men + 5 women = (6 x 5 / 3 + 5)

⇒ women = 15 women.

Now, if 5 women can do work in 6 days.

⇒ 15 women can do it in (5 x 6 / 15) days = 2 days

**Hence, 6 men and 5 women will take 2 days to finish the work.**

** Question 11: **4 men can do a piece of work in 10 days, 2 women can do it in 15 days and 5 children can do it in 12 days. In how many days can 8 men, 5 women and 15 children together complete the piece of work?

(1). 2 days

(2). 3 days

(3). 4 days

(4). 5 days

(5). None of these

**Answer: (5) None of these**

**Explanation:**

To given: 4 men’s 1 day’s work = 1 / 10.

1 man’s 1 day’s work = 1 / 40.

2 women’s 1 day’s work = 1 / 15.

1 woman’s 1 day’s work = 1 / 30.

5 children’s 1 day’s work = 1 / 12.

1 child’s 1 day’s work = 1 / 60.

To find: In how many days can 8 men, 5 women and 15 children together complete the piece of work?

Solution:

⇒ 4 men’s 1 day’s work = 1 / 10.

⇒ 1 man’s 1 day’s work = 1 / 40.

⇒ 2 women’s 1 day’s work = 1 / 15.

⇒ 1 woman’s 1 day’s work = 1 / 30.

⇒ 5 children’s 1 day’s work = 1 / 12.

⇒ 1 child’s 1 day’s work = 1 / 60.

Now,

⇒ (8 men + 5 women + 15 children)’s 1 day’s work = 8 / 40 + 5 / 30 + 15 / 60

⇒ (8 men + 5 women + 15 children)’s 1 day’s work = 1 / 5 + 1 / 6 + 1 / 4

⇒ (8 men + 5 women + 15 children)’s 1 day’s work = 37 / 60.

**So, they can finish the work in 60 / 37 days.**

**Question 12: **3 men can do a piece of work in 12 days, 5 women in 8 days and 20 children in 3 days. In how many days can a man, a woman, and a child work together to complete the piece of work?

(1). 12 days

(2). 13 days

(3). 14 days

(4). 15 days

(5). None of these

**Answer: (5). None of these**

**Explanation:**

To given: 3 men can do a piece of work in 12 days

5 women can do a piece of work in 8 days.

20 children can do a piece of work in 3 days.

To find: In how many days can a man, a woman, and a child work together to complete the piece of work?

Solution:

⇒ 3 men can do a piece of work in 12 days

⇒ 1 man will do the same piece of work in 36 days.

⇒ 5 women can do a piece of work in 8 days.

⇒ 1 woman will do the same piece of work in 40 days

⇒ 20 children can do a piece of work in 3 days.

⇒ 1 child will do the same piece of work in 60 days.

Now,

⇒ (1 man + 1 woman + 1 child)’s 1 day’s work = 1 / 36 + 1 / 40 + 1 / 60

⇒ (1 man + 1 woman + 1 child)’s 1 day’s work = 5 / 72.

**So, the work is complete in 72 / 5 days = 14 2 / 5 days**

**Question 13: **A certain number of men can complete a piece of work in 40 days. If there were 8 men more the work could be finished in 10 days less. How many men were there afterwards?

(1). 32 men

(2). 28 men

(3). 24 men

(4). 15 men

(5). None of these

**Answer: (1). 32 men**

**Explanation:**

Let the number of men be π₯.

π₯ men can do a work in 40 days.

(π₯ + 8) men can do the same work in (40 - 10) = 30 days.

⇒ π₯ x 40 = 30 (π₯ + 8)

⇒ 40π₯ = 30π₯ + 240

⇒ 40π₯ - 30π₯ = 240

⇒ 10π₯ = 240

⇒ π₯ = 24.

Therefore,

**The number of men afterwards = 24 + 8 = 32 men**

**Question 14: **If A can d0 ¼ of the work in 4 days and B can do β
of the work in 3 days, how much will A get if both work together and are paid Rs. 4,500 in all?

(1). Rs. 1,800

(2). Rs. 2,400

(3). Rs. 2,700

(4). Rs. 2,900

(5). None of these

**Answer: (3). Rs. 2,700**

**Explanation:**

Whole work is done by A in (4 x 4) days = 16 days

Whole work is done by Bin (8 x 3) days = 24 days.

A’s wages : B’s wages

⇒ A’s 1 day’s work : B’s 1 day's work

⇒ 1/16 : 1/24

⇒ 3 : 2

Therefore,

⇒ A’s sheet = (β x 4,500)

**⇒ A’s sheet = Rs. 2,700.**

**Question 15: **6 men can complete a piece of work in 12 days. 8 women can do the same piece of work in 18 days whereas 18 children can complete it in 10 days. 4 men, 12 women and 20 children work together for 2 days. If only men were to complete the remaining work in 1 day, how many men would be required totally?

(1). 36 men

(2). 24 men

(3). 18 men

(4). Cannot be determined

(5). None of these

**Answer: (1). 36 men**

**Explanation:**

⇒ (6 x 12) men = (8 x 18) women = (18 x 10) children.

⇒ 2 men = 4 women = 5 children

Now, 4 men + 12 women + 20 children = 4 men + 6 men + 8 men = 18 men

⇒ 6 men’s 1 day’s work = 1/12

⇒ 18 men’s 1 day’s work = 1/12 x 18/6 = ¼

⇒ 18 men’s 2 day’s work = ¼ x 2

⇒ 18 men’s 2 day’s work = ½

Therefore,

The remaining work = 1 - ½

⇒ remaining work = ½

Remaining work can be complete by 18 men in 2 days

**Therefore, to complete in 1 day, men required = 2 x 18 = 36 men**

Frequently Asked Questions

How can I improve my accuracy in the CLAT exam?

You can easily improve your speed and accuracy in the CLAT Exam by solving as many sample papers as possible. Practicing mock tests would definitely improve your time management skills and problem-solving techniques. So, it is advisable to solve mock tests on a daily basis.

Do I need to take specific coaching for CLAT Maths?

It solely depends on you whether you need to take CLAT coaching or not. If your fundamentals are strong, then it is easy to crack the exam just by solving previous year sample papers and Mock tests. However, if you want to improve your fundamentals then opting for coaching is beneficial.

What are the important topics of CLAT Maths Syllabus?

The important topics of CLAT Maths Syllabus are Profit & Loss, InterestNumber system, Surds & Indices, Ratio & Proportion, Percentage, HCF & LCM, and Interest.

What is the Difficulty level of Math Section in CLAT?

Based on the previous year's CLAT Exam Analysis, the Math Section's difficulty level was easy to moderate.

Is 1 month preparation enough for CLAT Maths Preparation?

Yes. With a proper preparation strategy, it is easy to prepare for the CLAT Mathematics section.