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Time and Work Questions: Time and Work is an important topic in the Quantitative Aptitude section of various competitive examinations such as CAT, GATE, Sarkari Naukri exams, etc. If you are looking for practice questions and tricks to master Time and Work topic, you have come to the right place.
With consistent practice and knowledge of shortcuts, you can easily crack this topic and score well in your schools exams, competitive exams or Sarkari Naukri exams. To help you in the process, we have provided some commonly asked questions in the exam along with formulas, concepts, and tricks to save you some time.
Introduction: Time and Work deals with the time taken by a person or a group of persons to complete a piece of work and the efficiency of the work done by each of them. There are two basic and main concepts in all time and work questions:
Note the following:
Let us understand the concept of time and work with an example.
Example: Worker A completes a task in 8 days, and worker B completes the same task in 10 days. If both A and B work together, in how many days they will complete the task?
Solution: Worker A completes the task in 8 days. So, in one day, he will complete 1/8 part of the task.
So, A’s one day work = 1/8
Similarly, B’s one day work = 1/10
∴ (A+B)’s one day work = 9/40
9/40 of the task is completed in one day so both will complete the whole task in 40/9 days.
The basic type of questions that may be asked in the exam with respect to the time and work topic are as follows:
Let’s see the formulas for each type of question asked from Time & Work concept.
Formulas can be very handy to solve questions on Time and Work as you can directly go to the solution part by just applying the correct formula. Some important Time and Work formulas are provided here for your reference:
In questions based on the man-days concept, we assume that all men work with equal efficiency unless stated otherwise in the question. The relation between the number of people working (N), the number of days worked (D), the number of hours worked per day (H) and the quantity of work (W) for two different cases is given below:
$${{{N_1} \times {D_1} \times {H_1}} \over {{W_1}}} = {{{N_2} \times {D_2} \times {H_2}} \over {{W_2}}}$$Important Points Regarding Work Equivalence Formulas:
We have provided some of the commonly asked questions on the Time and Work concept which will help students get an idea of what type of questions are asked in the competitive exam and what format and pattern are used for the same.
| Question 1: Rajan can do a piece of work in 24 days while Amit can do it in 30 days. In how many days can they complete it, if they work together? Solution: Work done by Rajan in 1 day = 1/24 Work done by Amit in 1 day = 1/30 Work done by Amit and Rajan together in 1 day = 1/24 + 1/30 = 54/720 = 3/40 ∴ They can complete the work in 40/3 days if they work together. |
| Question 2: Ravi can do a piece of work in 15 hours while Raman can do it in 12 hours. How long will both take to do it, working together? Solution: Time taken by Ravi = 15 hours Time taken by Raman = 12 hours Work done per hour by Ravi = 1/15 Work done per hour by Raman = 1/12 Work done per hour by Ravi and Raman together = 1/15 + 1/12 = 9/60 = 3/20 ∴ Time taken by Ravi and Raman together to finish the work = 20/3 hours. |
| Question 3: A and B, working together can finish a piece of work in 6 days, while A alone can do it in 9 days. How much time will B alone take to finish it? Solution: Time taken by A and B to finish a piece of work = 6 days Work done per day by A and B = 1/6 Time taken by A alone = 9 days Work done per day by A alone = 1/9 Work done per day by B = (Work done by A and B) – (Work done by A) = 1/6 – 1/9 1/18 ∴ B alone will take 18 days to complete the work. |
| Question 4: Two motor mechanics, Raju and Siraj, working together can overhaul a scooter in 6 hours. Raju alone can do the job in 15 hours. In how many hours can Siraj alone do it? Solution: Time taken by Raju = 15 h Work done by Raju in 1 hour = 1/15 Time taken by Raju and Siraj working together = 6 h Work done by Raju and Siraj in 1 h = 1/6 Work done by Siraj in 1 h = (Work done by Raju and Siraj) − (Work done by Raju) = 1/6−1/15 = 3/30 = 1/10 ∴ Siraj will take 10 h to overhaul the scooter by himself. |
| Question 5: A, B and C can do a piece of work in 10 days, 12 days and 15 days respectively. How long will they take to finish it if they work together? Solution: Time taken by A to complete the work = 10 days Time taken by B to complete the work = 12 days Time taken by C to complete the work = 15 days Work done per day by A = 1/10 Work done per day by B = 1/12 Work done per day by C = 1/15 Total work done per day = 1/10 + 1/12 + 1/15 = 15/60 = 1/4 ∴ A, B and C will take 4 days to complete the work if they work together. |
| Question 6: A can do a piece of work in 24 hours while B alone can do it in 16 hours. If A, B and C working together can finish it in 8 hours, in how many hours can C alone finish the work? Solution: Time taken by A to complete the piece of work = 24 h Work done per hour by A = 1/24 Time taken by B to complete the work = 16 h Work done per hour by B = 1/16 Total time taken when A, B and C work together = 8 h Work done per hour by A, B and C = 1/8 Work done per hour by A, B and C = (work done per hour by A) + (work done per hour by B) + (work done per hour by C) ∴ (Work done per hour by C) = (work done per hour by A, B and C) − (work done per hour by A) − (work done per hour by B) = 1/8 − 1/24 − 1/16 = 1/48 Thus, C alone will take 48 h to complete the work. |
| Question 7: A, B and C working together can finish a piece of work in 8 hours. A alone can do it in 20 hours and B alone can do it in 24 hours. In how many hours will C alone do the same work? Solution: A can complete the work in 20 h Work done per hour by A = 1/20 B can complete the work in 24 h Work done per hour by B = 1/24 It takes 8 h to complete the work if A, B and C work together. ∴ Work done together per hour by A, B and C = 1/8 (Work done per hour by A, B and C) = (work done per hour by A) + (work done per hour by B) + (work done per hour by C) OR (Work done per hour by C) = (work done per hour by A, B and C) − (work done per hour by A) − (work done per hour by B) = 1/8 − 1/24 − 1/20 = 1/30 ∴ C alone will take 30 h to complete the work. |
| Question 8: A and B can finish a piece of work in 16 days and 12 days respectively. A started the work and worked at it for 2 days. He was then joined by B. Find the total time taken to finish the work. Solution: Time taken by A to complete the work = 16 days Work done per day by A = 1/16 Time taken by B to complete the work = 12 days Work done per day by B = 1/12 Work done per day by A and B = 1/12 + 1/16 = 7/48 Work done by A in two days = 2/16 = 1/8 Work left =1 − 1/8 =7/8 A and B together can complete 7/48 of the work in 1 day. Then, time taken to complete 7/8 of the work = 7/8÷7/48 = 6 days ∴ Total time taken = 6 + 2 = 8 days. |
| Question 9: A can do a piece of work in 14 days while B can do it in 21 days. They began together and worked at it for 6 days. Then, A fell ill and B had to complete the remaining work alone. In how many days was the work completed? Solution: Time taken by A to complete the work = 14 days Work done by A in one day = 1/14 Time taken by B to complete the work = 21 days Work done by B in one day = 1/21 Work done jointly by A and B in one day =1/14 + 1/21 = 5/42 Work done by A and B in 6 days = 5/42 × 6 = 5/7 Work left = 1 − 5/7 = 2/7 With B working alone, time required to complete the work = 2/7 ÷ 1/21 = 2/7 × 21 = 2 × 3 = 6 days So, the total time taken to complete the work = 6 + 6 = 12 days |
| Question 10: A can do 2/3 of a certain work in 16 days and B can do 14 of the same work in 3 days. In how many days can both finish the work, working together? Solution: A can do 2/3 work in 16 days So, work done by A in one day = 2/48 = 1/24 B can do 14 work in 3 days So, work done by B in one day = 1/12 Work done jointly by A and B in one day = 1/24 + 1/12 = 1 + 2/24 = 3/24 = 1/8 So, A and B together will take 8 days to complete the work. |
| Question 11: A, B and C can do a piece of work in 15, 12 and 20 days respectively. They started the work together, but C left after 2 days. In how many days will the remaining work be completed by A and B? Solution: Time taken by A = 15 days Time taken by B = 12 days Time taken by C = 20 days Work done by A in one day = 1/15 Work done by B in one day = 1/12 Work done by C in one day = 1/20 Work done in one day by A, B and C together = 1/15 + 1/12 + 1/20 = 12/60 = 1/5 Work done by A, B and C together in 2 days = 2/5 Work remaining = 1 − 2/5 = 3/5 Work done by A and B in one day = 1/15 + 1/12 = 3/20 Time required by A and B to complete the remaining work together = 3/5 ÷ 3/20 = 4 days |
| Question 12: A and B can do a piece of work in 18 days; B and C can do it in 24 days while C and A can finish it in 36 days. In how many days can A, B, C finish it, if they all work together? Solution: Time needed by A and B to finish the work = 18 days Time needed by B and C to finish the work = 24 days Time needed by C and A to finish the work = 36 days Work done by A and B in one day = 1/18 Work done by B and C in one day = 1/24 Work done by C and A in one day = 1/36 2 × Work done by A, B and C in one day = 1/18 + 1/24 + 1/36 = 1/8 ∴ Work done by A, B and C in one day = 1/16 So, A, B and C working together will take 16 days to complete the work. |
| Question 13: A and B can do a piece of work in 12 days, B and C in 15 days, and C and A in 20 days. How much time will A alone take to finish the job? Solution: (A+B) can complete the work in 12 days (B+C) can complete the work in 15 days (C+A) can complete the work in 20 days (A+B)’s 1 day work = 1/12 (B+C)’s 1 day work = 1/15 (C+A)’s 1 day work = 1/20 2(A+B+C)’s 1 day work = 1/12 + 1/15 + 1/20 = 12/60 = 1/5 (A+B+C)’s 1 day work =1/10 A’s 1 day work = {(A+B+C)’s 1 day work} − {(B+C)’s 1 day work} = 1/10 − 1/15 = 1/30 A will take 30 days to complete the work, if he works alone. |
| Question 14: Pipes A and B can fill an empty tank in 10 hours and 15 hours respectively. If both are opened together in the empty tank, how much time will they take to fill it completely? Solution: A can fill a tank in 10 hours B can fill a tank in 15 hours Pipe A fills 1/10 of the tank in one hour Pipe B fills 1/15 of the tank in one hour Part of tank filled by pipes A and B together = 1/10 + 1/15 = 5/30 = 1/6 Thus, pipes A and B require 6 hours to fill the tank. |
| Question 15: Pipe A can fill an empty tank in 5 hours while pipe B can empty the full tank in 6 hours. If both are opened at the same time in the empty tank, how much time will they take to fill it up completely? Solution: Pipe A can fill a tank in 5 hours Pipe B can empty a full tank in 6 hours Pipe A fills 15 of the tank in one hour Pipe B empties 16 of the tank in one hour Part of the tank filled in one hour using both pipes A and B = 1/5 − 1/6 = 1/30 It takes 30 hours to fill the tank completely. |
| Question 16: Three taps A, B and C can fill an overhead tank in 6 hours, 8 hours and 12 hours respectively. How long would the three taps take to fill the empty tank, if all of them are opened together? Solution: Time taken by tap A to fill the tank = 6 hours Time taken by tap B to fill the tank = 8 hours Time taken by tap C to fill the tank = 12 hours A fills 1/6 of the tank in one hour B fills 1/8 of the tank in one hour C fills 1/12 of the tank in one hour Part of the tank filled in one hour using all the three pipes = 1/6 + 1/8 + 1/12 = 9/24 Time taken by A, B and C together to fill the tank = 24/9 = 8/3 hours |
| Question 17: A cistern has two inlets A and B which can fill it in 12 minutes and 15 minutes respectively. An outlet C can empty the full cistern in 10 minutes. If all the three pipes are opened together in the empty tank, how much time will they take to fill the tank completely? Solution: Inlet A can fill the cistern in 12 minutes Inlet B can fill the cistern in 15 minutes Outlet C empties the filled cistern in 10 minutes Part of the cistern filled by inlet A in one minute = 1/12 Part of the cistern filled by inlet B in one minute = 1/15 Part of the cistern emptied by outlet C in one minute = −1/10 (water flows out from C and empties the cistern) Part of the cistern filled in one minute with A, B and C working together = 1/12 + 1/15 − 1/10 = 1/20 The time required to fill the cistern with all inlets, A, B and C, open is 20 minutes. |
| Question 18: A pipe can fill a cistern in 9 hours. Due to a leak in its bottom, the cistern fills up in 10 hours. If the cistern is full, in how much time will it be emptied by the leak? Solution: A pipe can fill a cistern in 9 hours Part of the cistern filled by the pipe in one hour = 1/9 Let the leak empty the cistern in x hours Part of the cistern emptied by the leak in one hour = −1/x (The leak drains out the water) Considering the leak, the tank is filled in 10 hours Part of the tank filled in one hour = 1/10 Therefore, 1/9 − 1/x = 1/10 or, 1/x = 1/9 − 1/10 = 90 The leak will empty the filled cistern in 90 hours. |
| Question 19: Pipe A can fill a cistern in 6 hours and pipe B can fill it in 8 hours. Both the pipes are opened and after two hours, pipe A is closed. How much time will B take to fill the remaining part of the tank? Solution: Pipe A can fill a cistern in 6 hours Pipe B can fill a cistern in 8 hours Part of the cistern filled by pipe A in one hour = 1/6 Part of the cistern filled by pipe B in one hour = 1/8 Part of the cistern filled by pipes A and B in one hour = 1/6 + 1/8 = 7/24 Part of the cistern filled by pipes A and B in 2 hours = 7/24×2 = 7/12 Part of the tank empty after 2 hours = 1 − 7/12 = 5/12 Time taken by pipe B to fill the remaining tank = 5/12 ÷ 1/8 = 5/12×8 = 10/3 hours |
| Question 20: Fill in the blanks: (i) A tap can fill a tank in 6 hours. The part of the tank filled in 1 hour is ……… (ii) A and B working together can finish a piece of work in 6 hours while A alone can do it in 9 hours. B alone can do it in ……… hours. (iii) A can do a work in 16 hours and B alone can do it in 24 hours. If A, B and C working together can finish it in 8 hours, then C alone can finish it in ……… hours. (iv) If A’s one day’s work is 320, then A can finish the whole work in ……… days. Solution: (i) A tap can fill a tank in 6 hours. So, in 1 hour, 1/6 of the tank is filled. (ii) 18 hours (A+B)’s 1 hour work = 1/6 A’s 1 hour work =1/9 B’s 1 hour work = 1/6 − 1/9 = 1/18 Thus, B takes 18 hours to finish the work. (iii) 48 hours A’ s 1 hour work = 1/16 B’s 1 hour work = 1/24 C’s 1 hour work = 1/x (A+B+C)’s 1 hour work = 1/8 Therefore, 1/x = 1/8 − 1/16 − 1/24 = 1/48 or, x = 48 hours Thus, C alone takes 48 hours to complete the work. (iv) The time for completion is the reciprocal of the work done in one day. Therefore, A can complete the whole work in 20/3 days. |
Here are some of the practice questions on Time and Work concept to build your confidence:
Q1: Tick (✓) the correct answer:
(i) A alone can do a piece of work in 10 days and B alone can do it in 15 days. In how many days will A and B together do the same work?
(a) 5 days
(b) 6 days
(c) 8 days
(d) 9 days
(ii) A man can do a piece of work in 5 days. He and his son working together can finish it in 3 days. In how many days can the son do it alone?
(a) 13/2 days
(b) 7 days
(c) 15/2 days
(d) 8 days
(iii) A can do a job in 16 days and B can do the same job in 12 days. With the help of C, they can finish the job in 6 days only. Then, C alone can finish it in
(a) 34 days
(b) 22 days
(c) 36 days
(d) 48 days
(iv) To complete a work, A takes 50% more time than B. If together they take 18 days to complete the work, how much time shall B take to do it?
(a) 30 days
(b) 35 days
(c) 40 days
(d) 45 days
Q2: A can finish a work in 6 days and B can finish the same work in 8 days. A and B charge Rs. 2800 for the work. If with the help of C they complete the work in 3 days, how much they will pay to C?
Q3: 5 men undertook a piece of work and finished half the work in 18 days if two men drop out, in how many days the remaining work will be completed?
Q4: 2 men or 3 women can do a piece of work in 16 days. In how many days can 4 men and 6 women do the same work?
Q5: A group of workers undertakes a task. They can complete the task in 30 days. If 5 of them did not turn for the work and the remaining workers complete the task in 40 days, find the original number of workers.
Q6: A, B, C can do a job in 10, 20 and 40 days respectively. In how many days A can complete the job if he is assisted by B and C on every third day?
Q7: A can do a piece of work in 10 days. B is 50% more efficient than A. In how many days B alone can do the same job?
Q8: A can do a job in 30 days. B alone can do the same job in 20 days. If A starts the work and joined by B after 10 days, in how many days the job will be done?
Q9: A certain number of men can do a piece of work in 50 days. If there were 6 men more the same work could be done in 10 days less. Find the original number of men.
Q10: A is twice as good as workman as B and working together they can do a piece of work in 20 days. If A alone works, in how many days he will do the work?
Q11: A can finish a work in 10 days and B can finish the same work in 15 days. If they work alternatively, find the time taken to finish the job.
Q12: A, B, and C individually can finish a job in 10, 15, and 30 days respectively. If A starts the work and continues until the end, B and C work alternatively, in how many days work will be done?
Q13: A can finish a work in 8 hours, B can finish the same work in 12 hours, and C can do it in 24 hours. All the three starts work at 3 am, 4 am, and 5 am respectively. At what time work will be completed?
Q14: A and B work separately in 15 hours and 12 hours respectively. Another man C can destroy the work in 4 hours. If they start doing work at 8 am, 9 am, and 11 am respectively. At what time the total work will be destroyed?
Q15: A, B, and C together can complete a work in 6 days. The efficiency of A and C is 3 times of B, and the efficiency of A is 4 times of C, and then they alone can finish the job in how many days.
Q16: A man can finish a work in 20 days, a woman can finish the same work in 30 days, and a boy can finish the same work in 60 days. 2 men, 8 women, and some boys working together can finish the work in 2 days. Find how many boys are working?
Q17: A contractor undertakes to complete the job in 38 days. He assigns 30 workers on the job, and after 25 days he assigns 5 more workers and finishes the work one day before the given time. If he did not assign extra numbers of workers then work will be late by how many days.
Q18: A contractor undertakes to complete a work in 120 days with the help of 100 workers. After 45 days, he finds that only ¼ of the work has been completed. To complete the remaining work, how many extra workers will be required?
Q19: A, B, and C can finish a work in 18, 27, and 36 days respectively. All three start working together. A leaves the job after 8 days, and B leaves the job 6 days before it is finished, then the work will be finished in how many days?
Q20: Wages for 45 women amount to rupees 15525 in 48 days. How many men require to work 16 days to receive rupees 5750, the daily wages of a man being double of those of a woman?
To summarize the concept of Time and Work, we have provided all the important points to remember. This will help you solve all the questions related to Time and Work and its related concepts such as Pipes and Cisterns.
1. If a man can do a piece of work in n days, work done by him in one day = 1/n part of total work or he will finish 1/nth work in one day.
2. If a man completes 1/nth work in one day, he will complete the entire work in n days.
3. If A can complete a piece of work in X days and B can complete the same work in Y days, both A and B working together can finish the same work in XY/(X+Y) days.
4. If A is thrice as good as a workman as B or A can work three times faster than B, the ratio of work done by A and B for the same duration of time will be = 3 : 1. And the ratio of time taken by A and B to finish the same amount of work will be = 1: 3
5. A, B and C can do a work in D1, D2 and D3 days respectively. If they work for X1, X2 and X3 days respectively;
Here are some of the frequently asked questions on time and work questions.
| Q1: What is the relation between time and work? A: Time is directly proportional to the work. |
| Q2: Which is the best book to practice time and work questions? A: You can refer to materials provided on Embibe for for Time and Work or any standard book, but the best strategy to excel in this topic is to practice questions from the previous year papers and attempt quizzes as it will also help you to get familiar with the exam pattern for which you are preparing. |
| Q3: How to score well in time and work topic? A: The best way to score maximum marks in time and work topic is to practice as many questions as you can. You should also attempt mock tests available on Embibe for. |
| Q4: What is the weightage of Time and Work in different exams like SSC, CAT, Banking, and Railways? A: Time and Work require basic knowledge and understanding of Mathematics. So, it generally has a higher weightage as compared to other topics. Typically, 5-10% of questions are asked from this topic in different competitive exams. |
We hope this detailed article on Time and Work questions helps you. If you have any queries regarding this article, reach out to us through the comment section below and we will get back to you as soon as possible.
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