## CAT 2022 : Time and Work Practice Exercise-1

Welcome to this CAT Time and Work Questions exercise. In this five-question exercise, we build on the basic concepts for Time and Work. As you explore this topic, you will come across questions where situations such as time gaps and addition of an extra member to the group of workers are specified. Such questions need optimized tackling and can be solved with ease by using the formulas and understanding the relationships highlighted in the questions. This is where this simple and effective CAT Time and Work Questions exercise comes into the picture: it highlights the important concepts and tricks you should keep in mind for this question type.

**Question** **1**: There is a leak in the bottom of the tank. This leak can empty a full tank in 8 hr. When the tank is full, a tap is opened into the tank which intakes water at rate of 6 L per hour and the tank is now emptied in 12 hr. What is the capacity of the tank?

(a) 288 L

(b) 36 L

(c) 144 L

(d) Cannot be determined

### Answer and Explanation

Answers: (c)

Let the tap can fill the tank in x hours.

The rate of leak per hour = (1/8)

and rate of leak when the tap is on = (1 / 12).

Hence we have 1/8 – 1/x = 1/12 1/x = 1/8 – 1/12 = 2/48 = 1/24

i.e. the tap can fill the tank in 24 hours.

The tap fills at 6 litres per hour, so it will fill 6 × 24 = 144 litres in 24 hours.

Thus the capacity of the tank is 144 litres.

**Question 2:** A water tank has three tap: A, B and C. A fills 4 buckets in 24 min, B fills 8 buckets in 1 hr and C fills 2 buckets 20 min. If all the taps are opened together, a full tank is emptied in 2 hr. If a bucket contains 5 L water, what is the capacity of the tank?

(a) 120 L

(b) 240 L

(c) 180 L

(d) 60 L

### Answer and Explanation

**Question 3:** One man can do as much work in one day as a woman can do in 2 days. A child does one-third the work in a day as a woman. If an estate owner hires 39 pairs of hands—men, women and children in the ratio 6 : 5 : 2 and pays them in all Rs. 1, 113 at the end of the day’ s work, what must the daily wages of a child be, if the wages are proportional to the amount of work done ?

(a) Rs 14

(b) Rs 5

(c) Rs 20

(d) Rs 7

### Answer and Explanation

Answers: (d)

Ratio of number of men, women and children = 6 : 5 : 2 and the total number of men, women and children = 39.

Therefore the number of men = 18, women = 15 and children = 6.

Ratio of work done by men:women: children = 6 : 3 : 1

∴ Ratio of work done by 18 men, 15 women and 6 children

= (18 × 6) : (15 × 3) : (6 × 1) = 108 : 45 : 6

Hence Rs.1113 would be divided in this ratio.

That makes Rs756 for men, Rs 315 for women and Rs42 for children. Hence 6 children earn Rs42 in a day. So the daily

wage of a child is equal to 42/6 = Rs7

Hence, option d.

**Question 4:** Two typists undertake to do a job. The second typist begin working one hour after the first. Three hours after the first typist has begun working, there is still (9/20) of the work to be done. When the assignment is completed, it turns out that each typist has done half the work. How many hours would it take each one to do the whole job individually?

(a) 12 hr and 8 hr

(b) 8 hr and 5.6 hr

(c) 10 hr and 8 hr

(d) 5 hr and 4 hr

### Answer and Explanation

Answers: (c)

Let the first typist takex hours and second typist take y hours to do the whole job.

So 3 hours work of first typist and 2 hours work of second typist combined = 11/20

3/x + 2/y = 11/20 …(1)

Also it has been given that finally both have done the same amount of work.

x/2-y/(2 ) = 1 …(2)

From (1) and (2), we get x = 10 hours and y = 8 hours.

Hence, option c.

**Question 5:** A group of men decided to do a job in 8 days. But since 10 men dropped out every day, the job got completed at the end of the 12th day. How many men were there at the beginning?

(a) 165

(b) 175

(c) 80

(d) None of these

### Answer and Explanation

Answers: (a)

Let initially there were x men and each man can do 1 unit work in one day. As the work was to be completed in 8 days, so the total work is 8x.

Now every day, 10 workers dropped out. Hence we have

8x = x + (x – 10) + ( x – 20) ……. + (x – 110) = 12 (x – 55)

=>8x = 12x – 660

=>4x = 660

=>x = 165

Hence, option a.

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

- Time and Work is essentially a basic topic of commercial mathematics. It requires a clear understanding of basic concepts. You can explore school textbooks for this purpose.
- CAT Time and Work questions, where a time gap is given in the form of a tap closing or member leaving a group, can be tackled by using a few tricks. You should explore our concepts section for this topic in order to explore the various concepts probed in this topic.
- There are some basic pointers that you should keep in mind for CAT Time and Work questions. If you understand basic information provided in these questions and the kind of contexts that are built in these questions, then you will be able to solve these questions easily. For example, a couple of contexts you should keep in mind are:

1. If X and Y work together and Y leaves the job after a time period while another member Z joins the work. In such situations consider the entire job to be completed in ‘n’ days. Then find the portion of work done by each person with respect to ‘n’. From this you can find out the time taken by each person with respect to ‘n’.

2. Also, if a certain amount of work can be done by some members in ‘p’ days and more members are added then the work is done in less days.