## CAT 2022 : Time and Work Practice Exercise-2

This article for CAT Time and Work questions and answers provides you practice for this important commercial mathematics topics. Time work questions are somewhere analogous to ratio &proportions and the following set of CAT Time and Work questions and answers will show you the use of ratios in time and work questions. Here, the efficiency of a person to do the same work as compared to another is considered and used to deduce the answer.

**Question 1:** X does half of work what Y does in one sixth of the time. They take 10 days to complete a work together, how much time B take to do it alone?

(1) 70 days

(2) 30 days

(3) 40 days

(4) 50 days

### Answer and Explanation

Answer : (3)

Let Y does the whole work in a days ∴ Work done by Y in 1 day = 1/a According to question X does the ½ work in a/6 days

∴ A does the whole work in 2a/6 days = a/3 days ∴

Work done by X in one day = 3/a

∴ Work done by A and B together in one day =1/a+3/a = 4/a

∴ Time taken to complete the whole work by X and Y together = ¼ = a/4 days

Again, given that a/4 = 10 ∴ a = 40 days

**Question 2:** Shush and Komal can do a job together in 7 days. Shush is 7/4 times as efficient as Komal. The same job can be done by Shush alone in

(1) 49/4 days

(2) 49/3 days

(3) 11 days

(4) 28/3 days

### Answer and Explanation

Answer : (3)

Ratio of efficiency of Shush and Komal = 1:7/4 = 4:7

As the time taken is inversely proportional to efficiency, therefore,

if Komal takes 7x days to complete work, Asha will take 4x days.

Therefore 1/7x + 1/4x = 1/7 => (4+7)/28x = 1/7 ⇒ 28x = 11 × 7 Therefore x = {(11×7)/28} = 11/4

∴ Shush will complete the work in 4x = 4 (11/4) = 11 days.

**Question 3:** X is three times more efficient worker than Y is, therefore, able to complete a work in 60 days earlier. How many days will they take together to complete the work?

(1) 45/2

(2) 25

(3) 55/2

(4) 30

### Answer and Explanation

Answer : (1)

X is three times more efficient than Y.

It means if X takes ‘a’ days to complete a work, Y will take 3a days.

∴ 3a – a = 60 ⇒ a = 30 Hence, X takes 30 days to finish the work and Y takes 90 days.

When they work together (A + B)’s 1 day’s work = 1/30 +1/90 = (3+1)/90 = 4/90 = 2/45

∴ (X + Y) together can finish the work in 45/2 days

**Question 4:** X does half as much work as Y in one-sixth of the time. If to¬gether they take 10 days to com¬plete a work, how much time shall B alone take to do it ?

(1) 70 days

(2) 30 days

(3) 40 days

(4) 50 days

### Answer and Explanation

Answer : (3)

Suppose B takes x days to do the work Therefore A takes (2*1/6x) i.e, x/3 days to do it.

(A + B)’s 1 day’s work = Therefore 1/x + 3/x = 1/10

=> (1+3)/x = 1/10 => x = 40days

**Question 5:** Kamala can do a work in 15 days. Bimala is 50% more efficient than Kamala. The number of days, Bimala will take to do the same piece of work, is

(1) 14

(2) 12

(3) 10

(4) 21/2

### Answer and Explanation

Answer: (3)

As Bimala is 50% more efficient than Kamala so if kamala takes 3 days then Bimala take 2 days.

Time taken by Bimala =(2/3)*15 = 10days.

**Extra tips for CAT Time and Work Questions and Answers:**

• Complex Time and Work questions and answers can be simplified by using basic concepts of ratio and proportion and by understanding the relationship between the different aspects.

• Understand and analyze the question to find out what is asked and its relationship with what is given. By doing this, you can formulate an equation to find the correct answer.

• Important Note: Time taken is always inversely proportional to efficiency of doing the work.

i.e. If X is p times as efficientat working as Y, then Ratio of work done by X

and Y = p:1 and ratio of time taken is 1: p.

• Time and work questions related to efficiency may take some time but with practice they become easier to attempt.