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## CAT 2022 : Time and Work Practice Exercise-4

Welcome to this post on CAT Time and Work Problems. The objective of this post is very simple: to provide you vital practice for this topic and expose you to the kind of questions that you will encounter for this topic. Also, this CAT Time and Work exercise will help you practice 5 problems for this topic. In our concept section, we have gone through the basic concepts of time and work. Now let’s expand our knowledge further by solving CAT Time and Work problems. This section consists of problems related to real life time and work situations and needs the application of arithmetic concepts as well and strong logic. It consists of relative time, pairing of people to do the work and other such problems.

Question 1: Two full tanks, one shaped like a cylinder and the other like a cone, contain jet fuel. The cylindrical tank holds 500 L more than the conical tank. After 200 L of fuel has been pumped out from each tank, the cylindrical tank contains twice the amount of fuel in the conical tank. How many litres of fuel did the cylindrical tank have when it was full?
(a) 700 L
(b) 1,000 L
(c) 1,100 L
(d) 1,200 L

Let the volume of the conical tank bex L Then cylindrical tank will hold = (x +500) L

Given it is given, x +300 = 2 (x – 200) So, x +300 = 2x – 400 Therefore x = 700L.

Hence cylindrical tank will hold (700 + 500) = 1200 L of fuel.

Question 2: There’s a lot of work in preparing a birthday dinner. Even after the turkey is in the oven, there’re still the potatoes and gravy, yams, salad, and cranberries, not to mention setting the table. Three friendsAsit, Arnold, and Afzal, work together to get all of these chores done. The time it takes them to do the work together is six hours less than Asit would have taken working alone, one hour less than Arnold would have taken alone, and half the time Afzal would have taken working alone. How long did it take them to do these chores working together?
(a) 20 minutes
(b) 30 minutes
(c) 40 minutes
(d) 50 minutes

Let the time taken by Asit, Arnold and Afzal to complete the work alone be x, y and z hours respectively.

Given (x – 6) = (y – 1) = ⇒y = (x –5) and z = (2x – 12)

Also, time taken by all of them to do the job {(xyz)/(xy +yz+xz)} = (x-6)

Substitute y = (x – 5) and z = (2x – 12) in the above equation we get x = 20/3 hours.

∴ Time taken by all the three to complete the work. = 20/3-6 = 2/3hrs = 40 min.

Question 3: A can complete a piece of work in 4 days. B takes double the time taken by A, C takes double that of B, and D takes double that of C to complete the same task. They are paired in groups of two each. One pair takes two-thirds the time needed by the second pair to complete the work. Which is the first pair?
(a) A,B
(b) A,C
(c) B,C
(d) A, D

Working efficiency per day of A, B, C and D = ¼ , 1/8, 1/16 and 1/32 respectively.

Considering the options given, we have B and C does 3/16 of work per day, and A and D does 9/32 work per day.

Hence A and D take 32/9 days. B and C take 16/3 days.

Thus the first pair must comprise of A and D. Hence, option d.

Question 4: Three small pumps and a large pump are filling a tank. Each small pump works at 2/3rd the rate of the large pump. If all four work at the same time, they should fill the tank in what fraction of the time it would have taken the large pump alone?
(a) 4/7
(b) 1/3
(c) 2/3
(d) 3/4

Let the large pump rate be x. The time take by large pump = (1/x)

The small pumps rate would then be (2/3)x

When the four machines are combined their rate is x + (2/3)x + (2/3)x + (2/3)x = 3x.

So together they work 3 times as fast, so it will take 1/3 the time taken by the large pump alone.

Hence, option b

Question 5: Six technicians working at the same rate complete the work of one server in 10 hrs. If they start at 11 : 00 a.m. and one additional technician per hour being added beginning at 5 : 00 p.m., at what time the server will be complete ?
(a) 6 : 40 p.m.
(b) 7 p.m.
(c) 7 : 20 p.m.
(d) 8 : 00 p.m.

Since, six technicians working at the same rate completely work of one server in 10 hours.

Hence, total work = 10 × 6 = 60 man hours. Now, from 11.00 a.m. to 5 p.m. total man hours = 6 × 6 = 36

From 5 p.m. to 6 p.m. total man hours = 7, and the total hours of work completed would be 36 + 7 = 43

From 6 p.m. to 7 p.m. total man hours = 8, and the total hours of work completed would be 43 + 8 = 51

From 7 p.m. to 8 p.m. total man hours = 9 and the total hours of work completed would be 51 + 9 = 60

Hence, the work will be completed at 8 p.m.

Extra tips for CAT Time and Work Problems:
• CAT Time and work problems can be categorized into different types: First is to deduce the time taken and second it to find the amount of work done. Also, complex problems consist of many sub categories where relative time is to be considered and groups of people working together needs to be analyzed.
• An important formula you need to remember for solving such problems is as follows:
If A can do a work in ‘p’ hours and B can do the same work in ‘q’ hours, then if A and B work together the work done in 1 hour is 1/p+1/q.
• Also,Total Work= Total man hours = Number of men × Time taken for a job
• Time and work problems related to filling of tanks and pumps are very important. Practice them thoroughly in order to be prepared problems based from this area in the exam.

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