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GMAT Time and Work Problems with Solutions

Time and Work Problems with Solutions

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Are you desperately looking for practice questions on the GMAT club forum? How many questions did you find for the topic you were looking for? Are they any good?

Well, if you are scavenging for good practice questions you’ve just hit a gold mine! Problem solving comprises roughly 50% of the total questions in the GMAT quant section and in this blog, we are sharing some quality time and work problems along with their answers. Let’s go!

IN THIS BLOG:

1. Time and Problems: Difficulty Level I
2. Time and Problems: Difficulty Level II

Time and Work Problems: Difficulty Level – I

Given below are some time and work problems of medium-level difficulty along with their answers.

1. A, B and C individually can finish a work in 6, 8 and 15 hours respectively. They started the work together and after completing the work got INR 94.60 in all. When they divide the money among themselves, A, B, and C will respectively get (in INR):

  1. 44, 33, 17.60
  2. 43, 27.20, 24.40
  3. 45, 30, 19.60
  4. 42, 28, 24.60
  5. 41, 26.6, 29

Answer: A

2. Lewna got an order from a garment manufacturer for 480 denim shirts. He brought 12 sewing machines and appointed some expert tailors to do the job. However, many didn’t report to duty. As a result, each of those who did had to stitch 32 more shirts than originally planned by Lewna, with equal distribution of work. How many tailors had been appointed earlier and how many had not reported for work?

  1. 12, 4
  2. 10, 4
  3. 10, 3
  4. 10, 5
  5. None of these

Answer: C

3. Three machines, A, B, and C can be used to produce a product. Machine A will take 60 hours to produce a million units. Machine B is twice as fast as Machine A. Machine C will take the same amount of time to produce a million units as A and B running together. How much time will be required to produce a million units if all the three machines are used simultaneously?

  1. 12 hours
  2. 10 hours
  3. 8 hours
  4. 6 hours
  5. 7 hours

Answer: B

Direction for Question 4:

The question is followed by two statements. As the answer,
Mark (a) if the question can be answered with the help of a statement alone,
Mark (b) if the question can be answered with the help of statement II, alone,
Mark (c) if both, statement I and statement Il are needed to answer the question, and
Mark (d) if the question cannot be answered even with the help of both the statements.

4. Two types of widgets, namely type A and type B, are produced on a machine. The number of machine hours available per week is 80. How many widgets of type A must be produced?

  1. One unit of type A widget requires 2 machine hours and one unit of type B widget requires 4 machine hours.
  2. The widget dealer wants supply of at least 10 units of type A widget per week and he would not accept less than 15 units of type B widget.

Answer: C

5. A group of workers was put on a job. From the second day onwards, one worker was withdrawn each day. The job was finished when the last worker was withdrawn. Had no worker been withdrawn at any stage, the group would have finished the job in two-third the time. How many workers were there in the group?

  1. 2
  2. 3
  3. 5
  4. 11
  5. 6

Answer: B

6. 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 INR 1,113 at the end of the days’ work. What must the daily wages of a child be, if the wages are proportional to the amount of work done?

  1. 14
  2. 5
  3. 20
  4. 7
  5. 18

Answer: D

7. A water tank has three taps A, B, and C. A fills four buckets in 24 minutes, B fills 8 buckets in 1 hour and C fills 2 buckets in 20 minutes. If all the taps are opened together a full tank is emptied in 2 hours. If a bucket can hold 5 litres of water, what is the capacity of the tank?

  1. 120 litres
  2. 240 litres
  3. 180 litres
  4. 60 litres
  5. 45 litres

Answer: B

8. There is a leak in the bottom of the tank. This leak can empty a full tank in 8 hours. When the tank is full, a tap is opened into the tank which admits 6 litres per hour and the tank is now emptied in 12 hours. What is the capacity of the tank?

  1. 8 litres
  2. 36 litres
  3. 144 litres
  4. 136 litres
  5. Cannot be determined

Answer: C

9. 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?

  1. 165
  2. 175
  3. 80
  4. 90
  5. 120

Answer: A

10. Two typists undertake to do a job. The second typist begins 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?

  1. 12 hr and 8 hr
  2. 8 hr and 5.6 hr
  3. 10 hr and 8 hr
  4. 5 hr and 4 hr
  5. 4hr and 3 hr
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Directions for Questions 11 and 12: Answer the questions based on the following information.

The Weirdo Holiday Resort follows a particular system of holidays for its employees. People are given holidays on the days where the first letter of the day of the week is the same as the first letter of their names. All employees work at the same rate.

11. Raja starts working on February 25, 1996, and finishes the job on March 2, 1996. How much time would T and J take to finish the same job if both start on the same day as Raja?

  1. 4 days
  2. 5 days
  3. Either (a) or (b)
  4. Cannot be determined
  5. 6 days

Answer: C

12. Starting on February 25, 1996, if Raja had finished his job on April 2, 1996, when would T and S together likely to have completed the job, had they started on the same day as Raja?

  1. March 15, 1996
  2. March 14, 1996
  3. March 22, 1996
  4. March 29, 1996
  5. Data insufficient

Answer: C

13. A company has a job to prepare certain number of cans and there are three machines A, B and C for this job. A can complete the job in 3 days, B can complete the job in 4 days, and C can complete the job in 6 days. How many days will the company take to complete the job if all the machines are used simultaneously?

  1. 4 days
  2. 4/3 days
  3. 3 days
  4. 12 days
  5. 14 days

Answer: B

Time and Work Problems: Difficulty Level – II

Given below are some time and work problems of a higher level of difficulty along with their answers.

14. 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?

  1. A and B
  2. A and C
  3. B and C
  4. A and D
  5. C and D

Answer: D

15. There’s a lot of work in preparing a birthday dinner. Even after the turkey is in the oven, there’s still the potatoes and gravy, yams, salad, and cranberries, not to mention setting the table. Three friends — Asit, Arnold and Afzal — work together to get all of these chores done. The time it takes them to do the work together is 6 hr less than Asit would have taken working alone, 1 hr 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?

  1. 20 min
  2. 30 min
  3. 40 min
  4. 50 min
  5. 60 min

Answer: C

16. Three small pumps and a large pump are filling a tank. Each of the three small pumps works at 2/3th rate of the large pump. If all four pumps work at the same time, they should fill the tank in what fraction of the time that it would have taken the large pump alone?

  1. 4/7
  2. 1/3
  3. 2/3
  4. ¾
  5. 1/2

Answer: B

17. In the Nuts And Bolts factory, one machine produces only nuts at the rate of 100 nuts per minute and needs to be cleaned for 5 minutes after production of every 1000 nuts. Another machine produces only bolts at the rate of 75 bolts per minute and needs to be cleaned for 10 minutes after production of every 1500 bolts. If both the machines start production at the same time, what is the minimum duration required for producing 9000 pairs of nuts and bolts?

  1. 130 minutes
  2. 135 minutes
  3. 170 minutes
  4. 180 minutes
  5. 185 minutes

Answer: C

18. A chemical plant has four tanks (A, B, C and D), each containing 1000 litres of a chemical. The chemical is being pumped from one tank to another as follows:

From A to B @ 20 litres/minute
From C to A @ 90 litres/minute
From A to D @ 10 litres/minute
From C to D @ 50 litres/minute
From B to C @ 100 litres/minute
From D to B @ 110 litres/minute

Which tank gets emptied first, and how long does it take (in minutes) to get empty after pumping starts?

  1. A, 16.66
  2. C, 20
  3. D, 20
  4. D, 25
  5. A, 20

Answer: C

19. The radius of the cross-sections of pipes P1 and P2 are 7 m and 14 m respectively. Water flows through P1 at a constant rate of 10 m/s and it can alone fill a tank in 2 hours. If P1, is used as the inlet pipe and P2 as the outlet pipe then together they fill the tank in 4 hours. What is the rate of water flow (in m/s) through P2?

  1. 00
  2. 25
  3. 50
  4. 00
  5. 25

Answer: B

20. Anushka and Anirudh working together can complete a piece of work in 20 days. They started the work together, but Anushka left after x days and Anirudh finished the remaining work in the next x/2 days. Had Anushka left after 3x/4 days, Anirudh would have taken x days to finish the remaining work. Find the ratio of the efficiency of Anushka to that of Anirudh.

  1. 2:3
  2. 3:2
  3. 2:1
  4. 1:1
  5. 3:1

Answer: D

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