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40 Time and work Practice Questions with Solutions for CAT exam

Mastering Time and Work problems is essential for success in the CAT exam. By practicing the 40 questions and solutions provided in this article, you can enhance your problem-solving skills and increase your chances of scoring well in this challenging section.
authorImageAnil Solonki30 Jul, 2024
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40 Time and work Practice Questions with Solutions for CAT exam

CAT exam: Time and Work is an important topic in the Common Admission Test (CAT) that evaluates a candidate's ability to manage time efficiently and solve complex problems. In the CAT exam, time is of the essence, and mastering the art of solving time and work problems is essential to excel.

To help you ace this section, we have compiled 40 practice questions with detailed solutions to guide you through the process of solving them effectively.
Also Read
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CAT Admit Card 2024 CAT Exam Pattern 2024 CAT Syllabus 2024

Practice Questions with solutions on Time and Work

Here is the required Practice Questions with solutions on Time and Work listed below, candidates can practice from below:

Section I: Basic Time and Work Problems

  • A can complete a piece of work in 12 days, while B can complete the same work in 8 days. How long will it take for both A and B to complete the work together?
Solution: A's work rate: 1/12 per day B's work rate: 1/8 per day Combined work rate: 1/12 + 1/8 = 5/24 per day Time taken together: 24/5 days = 4.8 days
  • If 15 workers can complete a project in 20 days, how many workers are needed to finish the same project in 10 days?
Solution: Workers required = (15 * 20) / 10 = 30 workers
  • A and B together can complete a task in 8 days. If A can do the same task alone in 12 days, how long will it take B to complete the task alone?
Solution: A's work rate: 1/12 per day Combined work rate: 1/8 per day B's work rate = Combined work rate - A's work rate = (1/8) - (1/12) = 1/24 per day Time taken by B alone: 24 days
  • X can complete a job in 15 days, while Y can complete it in 20 days. How long will it take for X and Y to complete the job if they work on alternate days?
Solution: In one day, X completes 1/15 of the job, and Y completes 1/20. Together, they complete (1/15 + 1/20) = 7/60 of the job. Working on alternate days, they take twice as long: 2 * 60/7 = 17.14 days (approximately)

Section II: Complex Time and Work Problems

  • A group of 8 workers can build a wall in 12 days. If 2 workers quit after 4 days, how many additional days are required to complete the wall?
Solution: In 4 days, 8 workers complete 4 * 1/12 = 1/3 of the work. Remaining work = 1 - 1/3 = 2/3 With 6 workers (8 - 2), they can complete 6 * 2/3 = 4/3 of the work in one day. Additional days required = (2/3) / (4/3) = 1/2 day
  • P can paint a room in 6 hours, while Q can do it in 8 hours. How long will it take for both to paint the room if they work alternately for 1 hour each?
Solution: In one hour, P completes 1/6 of the work, and Q completes 1/8. Together, they complete (1/6 + 1/8) = 7/24 of the work in 1 hour. To complete the entire work, they need 24/7 hours.
  • A and B can complete a task in 20 days, while B and C can do it in 30 days. If A, B, and C work together, how long will it take to complete the task?
Solution: A + B complete 1/20 of the work in one day. B + C completes 1/30 of the work in one day. Adding these rates together: A + 2B + C complete 1/20 + 1/30 = 1/12 of the work in one day. A, B, and C together complete 1/12 * 12 = 1 work in one day. So, it will take them 1 day to complete the task together.

Section III: CAT-Level Time and Work Problems

  • A factory has 5 machines that can produce 1000 toys in 5 hours. How many toys can 10 machines produce in 8 hours?
Solution: The rate of 5 machines = 1000 toys/5 hours = 200 toys/hour So, the rate of 1 machine = 200 toys/hour Rate of 10 machines = 10 * 200 toys/hour = 2000 toys/hour In 8 hours, 10 machines can produce 2000 toys/hour * 8 hours = 16,000 toys.
  • Ramesh can complete a project in 10 days working 8 hours a day. How many hours a day should he work to finish the project in 5 days?
Solution : Ramesh's total work = 10 days * 8 hours/day = 80 hours To complete the project in 5 days, he needs to work 80 hours / 5 days = 16 hours a day.
  • A can do a certain job in 10 days, while B can do it in 12 days. They both start the work together, but after 2 days, A leaves. How many more days will B take to complete the job?
Solution : In 2 days, A and B complete 2 * [(1/10) + (1/12)] = 11/30 of the work. Remaining work = 1 - 11/30 = 19/30 Now, B can complete the remaining work in (19/30) / (1/12) = 38/5 days = 7.6 days.
  1. If a pump can empty a tank in 9 hours, and another pump can empty it in 12 hours, how long will it take to empty the tank if both pumps operate simultaneously?
Solution: The first pump's rate = 1/9 per hour, and the second pump's rate = 1/12 per hour. Together, their rate = (1/9) + (1/12) = 4/36 + 3/36 = 7/36 per hour. To empty the tank, it takes 36/7 hours, which is approximately 5.14 hours.
  1. A can complete a task in 9 hours, and B can complete the same task in 12 hours. How long will it take for A to complete half the task, and then B to complete the other half?
Solution : A's rate = 1/9 per hour, B
  1. If 8 workers can build a house in 40 days, how many days will it take for 12 workers to build the same house?
Solution : The rate of 8 workers = 1/40 per day. To find the number of days for 12 workers, we need to find the rate of 12 workers. Rate of 12 workers = (1/40) * (12/8) = 3/10 per day. To complete the house, it takes 10/3 days, which is approximately 3.33 days.
  1. A group of 4 people can complete a task in 12 days. How many people are needed to complete the same task in 6 days?
Solution : Let's assume the total work is W. Work rate of 4 people = W/12, work rate of N people (where N is the number needed) = W/6. Equate the work rates: W/12 = W/6N. Solve for N: N = 2.
  1. A can do a piece of work in 5 days, B can do it in 6 days, and C can do it in 10 days. How long will it take for all three working together to complete the work?
Solution : A's rate = 1/5 per day, B's rate = 1/6 per day, C's rate = 1/10 per day. Together, their rate = (1/5) + (1/6) + (1/10) = (12/60) + (10/60) + (6/60) = 28/60 per day. To complete the work, they need 60/28 days, which is approximately 2.14 days.
  1. A machine can fill a tank in 6 hours, and another machine can empty the tank in 8 hours. If both machines operate simultaneously, how long will it take to fill the tank?
Solution : The filling machine's rate = 1/6 per hour, and the emptying machine's rate = -1/8 per hour (negative because it's emptying). Together, their rate = (1/6) - (1/8) = 4/24 - 3/24 = 1/24 per hour. To fill the tank, it takes 24 hours.
  1. A can complete a task in 12 days, and B can complete the same task in 15 days. How long will it take for both A and B to complete the task if they work together?
Solution : A's work rate = 1/12 per day, B's work rate = 1/15 per day. Together, their work rate = (1/12) + (1/15) = 9/60 = 3/20 per day. To complete the task, they need 20/3 days, which is 6 days and 2/3 days.
  1. If 5 men can complete a project in 10 days, how many days will it take for 8 men to complete the same project?
Solution : Let the total work be W. Work rate of 5 men = W/10, work rate of 8 men = W/D (where D is the number of days needed). Equate the work rates: W/10 = 8W/D. Solve for D: D = 8 * 10 = 80 days.
  1. A and B can complete a job in 15 days, while B and C can complete the same job in 20 days. How long will it take for A, B, and C to complete the job together?
Solution : Let's find A's, B's, and C's work rates: A and B together take 15 days, so their combined rate = 1/15. B and C together take 20 days, so their combined rate = 1/20. Now, A, B, and C together: (A's rate + B's rate + C's rate) = (1/15 + 1/20 + C's rate). Solve for C's rate: C's rate = 1/15 + 1/20 - 1/12 = 1/60. Now, to complete the job, they need 60 days.
  1. A can build a wall in 10 days, B can build the same wall in 15 days, and C can build it in 20 days. How long will it take for all three working together to complete the wall?
Solution : A's rate = 1/10 per day, B's rate = 1/15 per day, and C's rate = 1/20 per day. Together, their rate = (1/10) + (1/15) + (1/20) = 6/60 + 4/60 + 3/60 = 13/60 per day. To complete the wall, they need 60/13 days, which is approximately 4.62 days.

20 Tough Questions on Time and Work for CAT 2024

  1. A can complete a job in 8 days, B can complete it in 10 days, and C can complete it in 12 days. How long will it take for A, B, and C to complete the job together?
Solution: A's rate = 1/8 per day, B's rate = 1/10 per day, C's rate = 1/12 per day. Together, their rate = (1/8) + (1/10) + (1/12) = 15/120 + 12/120 + 10/120 = 37/120 per day. To complete the job, they need 120/37 days, which is approximately 3.24 days.
  1. A and B can complete a job in 15 days, B and C can complete it in 20 days, and C and A can complete it in 30 days. How long will it take for A, B, and C to complete the job together?
Solution: Let's denote A's, B's, and C's rates as A, B, and C, respectively. We can set up three equations based on the given information:
  • A + B = 1/15
  • B + C = 1/20
  • C + A = 1/30
Adding these equations together: 2(A + B + C) = 1/15 + 1/20 + 1/30 = (4 + 3 + 2)/60 = 9/60 = 3/20 Now, A + B + C = (3/20) / 2 = 3/40. To complete the job, they need 40/3 days, which is approximately 13.33 days.
  1. A can complete a task in 24 days, while B can complete the same task in 16 days. They start working together but after 6 days, A leaves. How many more days will B take to complete the task?
Solution: In 6 days, A completes 6/24 = 1/4 of the task. So, 3/4 of the task is left. B's rate = 1/16 per day. To complete 3/4 of the task, B will take (3/4) / (1/16) = 12 days. Therefore, B will take an additional 12 days to complete the task.
  1. If 5 men and 3 women can complete a job in 10 days, and 4 men and 6 women can complete it in 8 days, how long will it take for 7 men and 2 women to complete the job?
Solution: Let M represent the work rate of a man per day, and W represent the work rate of a woman per day. We can set up two equations based on the given information: 5M + 3W = 1/10 (Work rate of 5 men and 3 women) 4M + 6W = 1/8 (Work rate of 4 men and 6 women) Solve these equations to find M and W: M = 1/20 (Work rate of a man) W = 1/60 (Work rate of a woman) Now, we need to find the work rate of 7 men and 2 women: 7M + 2W = (7/20) + (2/60) = (21/60) + (2/60) = 23/60 To complete the job, they need 60/(23/60) days, which is approximately 23.48 days.
  1. A, B, and C can complete a task in 6, 8, and 12 days, respectively. How long will it take for A and B to complete half the task, and then C to complete the other half?
Solution: A's rate = 1/6 per day, B's rate = 1/8 per day, C's rate = 1/12 per day. Together, A and B's rate = (1/6) + (1/8) = (4/24) + (3/24) = 7/24 per day. To complete half the task, they need (1/2) / (7/24) days, which is approximately 6 days. Now, C's rate is 1/12 per day, and they have 1/2 of the task left. To complete the other half, it will take (1/2) / (1/12) days, which is 6 days. So, in total, it will take 6 + 6 = 12 days to complete the entire task.
  1. A, B, and C can complete a task in 9 days, 12 days, and 15 days, respectively. They start working together, but after 3 days, A leaves. How long will it take for B and C to complete the remaining work?
Solution: A's rate = 1/9 per day, B's rate = 1/12 per day, C's rate = 1/15 per day. Together, their rate = (1/9) + (1/12) + (1/15) = (4/36) + (3/36) + (2/30) = 9/36 = 1/4 per day. In 3 days, A completes (3 * 1/9) = 1/3 of the work. So, 2/3 of the work is left. Now, B and C's combined rate = (1/12) + (1/15) = (5/60) + (4/60) = 9/60 = 3/20 per day. To complete 2/3 of the work, B and C will take (2/3) / (3/20) days, which is approximately 13.33 days.
  1. A can do a job in 8 days, B can do it in 10 days, and C can do it in 12 days. They start working together, but every day, A and B take a day off, while C works. How long will it take for them to complete the job?
Solution: A's rate = 1/8 per day, B's rate = 1/10 per day, C's rate = 1/12 per day. Together, their rate = (1/8) + (1/10) + (1/12) = (5/40) + (4/40) + (3/40) = 12/40 = 3/10 per day. Every day, 2/10 of the job is completed (since A and B take a day off). So, they complete 1/10 of the job each day. To complete the entire job, it will take 10 days.
  1. A can complete a job in 5 days, B can complete it in 8 days, and C can complete it in 12 days. They start working together, but after 4 days, C leaves. How long will it take for A and B to complete the remaining work?
Solution: A's rate = 1/5 per day, B's rate = 1/8 per day, C's rate = 1/12 per day. Together, their rate = (1/5) + (1/8) + (1/12) = (8/40) + (5/40) + (3/40) = 16/40 = 2/5 per day. In 4 days, A, B, and C together complete (4 * 2/5) = 8/5 of the work. So, (5 - 8)/5 = -3/5 of the work is left. Now, A and B's combined rate is (1/5) + (1/8) = (8/40) + (5/40) = 13/40 per day. To complete the remaining work, A and B will take (-3/5) / (13/40) days, which is approximately 2.15 days.
  1. A can complete a job in 15 days, B can complete it in 12 days, and C can complete it in 10 days. They start working together but after 4 days, A leaves. How many more days will it take for B and C to complete the remaining work?
Solution: A's rate = 1/15 per day, B's rate = 1/12 per day, C's rate = 1/10 per day. Together, their rate = (1/15) + (1/12) + (1/10) = (4/60) + (5/60) + (6/60) = 15/60 = 1/4 per day. In 4 days, A completes (4 * 1/15) = 4/15 of the work. So, 11/15 of the work is left. Now, B and C's combined rate = (1/12) + (1/10) = (5/60) + (6/60) = 11/60 per day. To complete 11/15 of the work, B and C will take (11/15) / (11/60) days, which is approximately 4 days.
  1. A can complete a job in 10 days, B can complete it in 15 days, and C can complete it in 20 days. They start working together but after 5 days, A and B leave. How long will it take for C to complete the remaining work?
Solution: A's rate = 1/10 per day, B's rate = 1/15 per day, C's rate = 1/20 per day. Together, their rate = (1/10) + (1/15) + (1/20) = (3/30) + (2/30) + (1/20) = 6/60 + 4/60 + 3/60 = 13/60 per day. In 5 days, A and B together complete (5 * 13/60) = 13/12 of the work. So, 1/12 of the work is left. Now, C's rate is 1/20 per day. To complete 1/12 of the work, C will take (1/12) / (1/20) days, which is 5 days.
  1. A can complete a job in 12 days, B can complete it in 18 days, and C can complete it in 24 days. They start working together but after 6 days, C leaves. How long will it take for A and B to complete the remaining work?
Solution: A's rate = 1/12 per day, B's rate = 1/18 per day, C's rate = 1/24 per day. Together, their rate = (1/12) + (1/18) + (1/24) = (2/24) + (3/24) + (1/24) = 6/24 = 1/4 per day. In 6 days, A, B, and C together complete (6 * 1/4) = 3/2 of the work. So, 1/2 of the work is left. Now, A and B's combined rate is (1/12) + (1/18) = (3/36) + (2/36) = 5/36 per day. To complete 1/2 of the work, A and B will take (1/2) / (5/36) days, which is 18/5 days, or approximately 3.6 days.
  1. A can complete a job in 9 days, B can complete it in 12 days, and C can complete it in 15 days. They start working together, but every 2 days, A takes a day off, and every 3 days, B takes a day off. How long will it take for them to complete the job?
Solution: A's rate = 1/9 per day, B's rate = 1/12 per day, C's rate = 1/15 per day. Together, their rate = (1/9) + (1/12) + (1/15) = (4/36) + (3/36) + (2/36) = 9/36 = 1/4 per day. Every 2 days, A takes a day off, so effectively, A works 1 out of every 3 days. Every 3 days, B takes a day off, so effectively, B works 2 out of every 3 days. In 3 days, they complete (3 * 1/4) = 3/4 of the work. So, 1/4 of the work is left. Now, A and B's combined rate is (1/9) + (1/12) = (4/36) + (3/36) = 7/36 per day. To complete 1/4 of the work, A and B will take (1/4) / (7/36) days, which is approximately 5.14 days.
  1. A can complete a job in 16 days, B can complete it in 20 days, and C can complete it in 24 days. They start working together, but after 8 days, A leaves. How long will it take for B and C to complete the remaining work?
Solution: A's rate = 1/16 per day, B's rate = 1/20 per day, C's rate = 1/24 per day. Together, their rate = (1/16) + (1/20) + (1/24) = (5/80) + (4/80) + (3/80) = 12/80 = 3/20 per day. In 8 days, A, B, and C together complete (8 * 3/20) = 12/20 of the work. So, 8/20 of the work is left, which simplifies to 2/5. Now, B and C's combined rate is (1/20) + (1/24) = (3/60) + (2/60) = 5/60 per day. To complete 2/5 of the work, B and C will take (2/5) / (5/60) days, which is approximately 24 days.
  1. A, B, and C can complete a task in 8, 12, and 16 days, respectively. They start working together, but after 4 days, A and B leave. How long will it take for C to complete the remaining work?
Solution: A's rate = 1/8 per day, B's rate = 1/12 per day, C's rate = 1/16 per day. Together, their rate = (1/8) + (1/12) + (1/16) = (3/24) + (2/24) + (1/24) = 6/24 = 1/4 per day. In 4 days, A, B, and C together complete (4 * 1/4) = 1/4 of the work. So, 3/4 of the work is left. Now, C's rate is 1/16 per day. To complete 3/4 of the work, C will take (3/4) / (1/16) days, which is 12 days.
  1. A, B, and C can complete a job in 10, 15, and 20 days, respectively. They start working together, but after 5 days, A leaves. How long will it take for B and C to complete the remaining work?
Solution: A's rate = 1/10 per day, B's rate = 1/15 per day, C's rate = 1/20 per day. Together, their rate = (1/10) + (1/15) + (1/20) = (3/30) + (2/30) + (1/30) = 6/30 = 1/5 per day. In 5 days, A, B, and C together complete (5 * 1/5) = 1 of the work. So, 4/5 of the work is left. Now, B and C's combined rate is (1/15) + (1/20) = (4/60) + (3/60) = 7/60 per day. To complete 4/5 of the work, B and C will take (4/5) / (7/60) days, which is approximately 17.14 days.
  1. A, B, and C can complete a job in 9, 12, and 18 days, respectively. They start working together, but after 3 days, C leaves. How long will it take for A and B to complete the remaining work?
Solution: A's rate = 1/9 per day, B's rate = 1/12 per day, C's rate = 1/18 per day. Together, their rate = (1/9) + (1/12) + (1/18) = (4/36) + (3/36) + (2/36) = 9/36 = 1/4 per day. In 3 days, A, B, and C together complete (3 * 1/4) = 3/4 of the work. So, 1/4 of the work is left. Now, A and B's combined rate is (1/9) + (1/12) = (4/36) + (3/36) = 7/36 per day. To complete 1/4 of the work, A and B will take (1/4) / (7/36) days, which is approximately 9 days. These problems require careful calculation and understanding of work rates to solve efficiently.
  1. A can complete a job in 6 days, B can complete it in 8 days, and C can complete it in 12 days. They start working together, but after 4 days, A and B leave. How long will it take for C to complete the remaining work?
Solution: A's rate = 1/6 per day, B's rate = 1/8 per day, C's rate = 1/12 per day. Together, their rate = (1/6) + (1/8) + (1/12) = (4/24) + (3/24) + (2/24) = 9/24 = 3/8 per day. In 4 days, A, B, and C together complete (4 * 3/8) = 3/2 of the work. So, 1/2 of the work is left. Now, C's rate is 1/12 per day. To complete 1/2 of the work, C will take (1/2) / (1/12) days, which is 6 days.
  1. A, B, and C can complete a task in 7, 10, and 14 days, respectively. They start working together, but after 6 days, A leaves. How long will it take for B and C to complete the remaining work?
Solution: A's rate = 1/7 per day, B's rate = 1/10 per day, C's rate = 1/14 per day. Together, their rate = (1/7) + (1/10) + (1/14) = (20/140) + (14/140) + (10/140) = 44/140 = 11/35 per day. In 6 days, A, B, and C together complete (6 * 11/35) = 66/35 of the work. So, (35 - 66)/35 = -31/35 of the work is left. Now, B and C's combined rate is (1/10) + (1/14) = (7/70) + (5/70) = 12/70 = 6/35 per day. To complete the remaining work, B and C will take (-31/35) / (6/35) days, which is approximately 5.17 days.
  1. A can complete a job in 9 days, B can complete it in 12 days, and C can complete it in 18 days. They start working together, but after 3 days, A and B leave. How long will it take for C to complete the remaining work?
Solution: A's rate = 1/9 per day, B's rate = 1/12 per day, C's rate = 1/18 per day. Together, their rate = (1/9) + (1/12) + (1/18) = (4/36) + (3/36) + (2/36) = 9/36 = 1/4 per day. In 3 days, A, B, and C together complete (3 * 1/4) = 3/4 of the work. So, 1/4 of the work is left. Now, C's rate is 1/18 per day. To complete 1/4 of the work, C will take (1/4) / (1/18) days, which is 4.5 days. These problems involve variations in work rates and time frames, making them suitable for advanced practice in time and work concepts.
  1. A can complete a job in 8 days, B can complete it in 12 days, and C can complete it in 24 days. They start working together, but after 6 days, A leaves. How long will it take for B and C to complete the remaining work?
Solution: A's rate = 1/8 per day, B's rate = 1/12 per day, C's rate = 1/24 per day. Together, their rate = (1/8) + (1/12) + (1/24) = (3/24) + (2/24) + (1/24) = 6/24 = 1/4 per day. In 6 days, A, B, and C together complete (6 * 1/4) = 3/2 of the work. So, 1/2 of the work is left. Now, B and C's combined rate is (1/12) + (1/24) = (2/24) + (1/24) = 3/24 = 1/8 per day. To complete 1/2 of the work, B and C will take (1/2) / (1/8) days, which is 4 days. CAT is a highly competitive entrance exam. Candidates aiming to excel in the CAT exam 2024 must prepare rigorously. To help candidates outperform their competitors and secure a commendable 99 percentile, PW MBA Online Coaching provides expert guidance and comprehensive syllabus coverage. Additionally, PW faculties conduct regular evaluations and encourage them to strengthen their weak areas.

40 Time and work Questions with Solutions for CAT FAQs

What is the significance of practicing time and work questions for the CAT exam?

Practicing time and work questions for the CAT exam helps you improve your problem-solving skills, logical reasoning, and time management abilities. These questions often appear in the Quantitative Ability section, making them crucial for a competitive score.

How can I approach time and work questions effectively during CAT preparation?

To approach time and work questions effectively, understand the concept of work rates, set up equations based on the given information, and solve them systematically. Practice various scenarios to develop a deep understanding of different problem types.

What should I do if I get stuck on a particular time and work question during practice?

If you get stuck on a time and work question, don't dwell on it for too long. Move on to the next question and come back to it later if time permits. Sometimes, solving other questions can give you insights on how to tackle the challenging one.

Are there any shortcuts or tricks for solving time and work questions in the CAT exam?

While there are no shortcuts, you can use efficient techniques like setting up ratios and equations, breaking complex tasks into smaller parts, and looking for patterns to simplify calculations. Practice will help you develop these skills.

How can I ensure I'm well-prepared for time and work questions in the CAT exam?

To ensure you're well-prepared, regularly practice a variety of time and work problems. Review your mistakes and learn from them. Additionally, consider taking mock tests to simulate exam conditions and track your progress. This will help you build confidence and proficiency in solving these questions.
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