Time and Work Questions for Aptitude Exams 2022

Time and work is a really important topic for the aptitude exams. Questions based on this concept have been appearing regularly over the past decade in different aptitude exams like DUJAT, IPMAT etc. On average, you will have 2-3 questions based on this topic every year in Management Aptitude Entrance examinations. To ease out your preparation, we have aggregated important time and work Questions for the Aptitude Exams from the previous year's papers and a few self-designed questions by TopRankers faculty.

Time and Work Concept

To solve these questions first we need to understand the basic concept of work. Say for example if A does a work in ‘a’ days, then in one day A does ⇒1/a work. If B does work in ‘b’ days, then in one day B does ⇒ 1/b work. So if A and B work together then their combined work is 1/a + 1/b = (a+b)/ab Example. If A can do a work in 10 days and B can do the same work in 12 days, then the work will be completed in how many days.

Solution. Total no. of days = (10*12)/(22) = 120/22 = 5.45 days

Instead of taking the value of the total work as 1 unit of work, we can also look at the total work as the relative percentage of work done in a day. If A does work in 10 days, then in one day he will do 10% of the total work.

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Example2:

A can build a wall in 10 days and B can build it in 5 days, while C can destroy it in 20 days. If they start working in how many days will the work be completed?

Solution:

The net combined work per day = A’s work + B’s work - C’s work

⇒ 10% + 20% - 5%

⇒ 25% in one day

⇒100/25 = 4 days.

The general equation that applies to Time and Work problem is

⇒ work rate x time = work done

According to this equation if work done is constant then the work rate is inversely proportional to time. But if the work done changes then there is a change in the product of work rate and time. If the work is doubled and time is halved then the work rate is increased by four times. 

Example 3:

20 men working 8 hours a day can completely build a wall of length 200 meters, breadth 10 metres and height 20 metres in 10 days. How many days will 25 men working 12 hours a day require to build a wall of length 400 meters, breadth 10 metres and height of 15 metres?

Solution:

L1B1H1/ L2B2H2 = m1t1d1/ m2t2d2

(200* 10 * 20) / (400 * 10 * 15) = (20 * 8 *10) / (25 * 12 * d2)

⇒ d2 = 8 days,

Important Time and Work Questions for Aptitude Exams

Q1. 'A' can do a piece of work in 25 days and B in 20 days. They work together for 5 days and then 'A' goes away. In how many days will B' finish the remaining work? 

(a) 17 days (b) 11 days (c) 10 days (d) None of these

Solution

Percentage of work done by A in one day = 100/25 = 4%

⇒ Percentage of work done by A in one day = 100/20 = 5%

⇒ Work done by both of them in 5 days = 4*5 + 5*5 = 45% work.

⇒ work left to be done = 100 - 45 = 55%

⇒ days taken by B to complete 55% work = 55/5 = 11 days.

Hence option B is the correct choice.

Q2. A can do work in 18 days, B in 9 days and C in 6 days. A and B start working together and after 2 days C joins them. What is the total number of days taken to finish the work? 

(a) 4.33 (b) 4.5 (c) 4.66 (d) None of these

Solution

Percentage of work done by A in one day = 100/18 = 5.55%

⇒ Percentage of work done by A in one day = 100/9 = 11.11%

⇒ Percentage of work done by C in one day = 100/6 = 16.66%

⇒ Work done by A and B in 2 days = 2*5.55 + 2*11.11 = 33.32% work.

⇒ work left to be done = 100 - 33.32 = 66.68%

⇒ days taken by all of them to complete 66.68% work = 66.68/33.32 = 2 days.

⇒ Total no. of days = 4 days.

Hence option D is the correct choice.

Q3. A and B required 10 days to complete a job. B and C require 12 days to complete the same job. A and C require 15 days to complete the same job. The number of days required, if all are at work, to compete the job is 

(a) 8 days (b) 9 days (c) 6 days (d) 7 days

Solution

Percentage of work done by A and B in one day = 100/10 = 10%

⇒ Percentage of work done by B and C in one day = 100/12 = 8.34%

⇒ Percentage of work done by A and C in one day = 100/15 = 6.66%

⇒ Work done by A, B and C in one day = 2(a + b + c) = 25% ⇒12.5%

⇒ Total no. of days to complete the work= 100/12.5 = 8 days.

Hence option D is the correct choice.

Q4. If Ajit can do one-fourth of a work in 3 days and Sujit can do one-sixth of the same work in 4 days, how much will Ajit get if both work together and are paid Rs. 180 in all? 

(a) Rs. 120 (b) Rs. 108 (c) Rs. 60 (d) Rs. 36

Solution

Work done by ajit in one day = 100/4*3 = 8.33.

Work done by Sujit in one day = 100/ 6*4 = 4.167

The ration of Ajit and Sujit Work ⇒ 8.33: 4.12 ⇒ 2:1

Therefore Ajit will be paid = 180*2 / 3 = 120.

Hence option A is the correct choice.

Q5. A can-do work in 9 days. If B is 50% more efficient than A, then in how many days can B do the same work?

(a)13.5 (b) 4.5 (c) 6 (d) 3

Solution

⇒ Percentage of work done by A in one day = 100/9 = 11.11%

⇒ Percentage of work done by B in one day = 11.11 + 11.11*(.5) = 16.66%

⇒ Total no. of days taken by B to complete the work= 100/16.66 = 6 days.

Hence option C is the correct choice.

Q6. Two men undertake to do a piece of work for Rs. 200. One alone can do it

in 6 days and the other in 8 days. With the help of a boy, they finish it in 3 days. How much is the share of the boy?

(a) Rs. 45 (b) Rs. 40 (c) Rs. 30 (d) Rs. 25

Solution

Let the total work be the LCM of 6 and 8 i.e 24 units.

⇒ Work done by A will be 4 units per day

⇒ work done by B will be 3 units per day

⇒ total work be 8 units day

⇒ therefore the work done by boy will be 8 - 7 ⇒ 1 unit per day

⇒ the boy will be paid ⅛ x 200 = Rs. 25.

Hence option D is the correct choice. 

Q7. 10 men and 15 women together can complete a work in 6 days. It takes

100 days for one man alone to complete the same work. How many days will be required for one woman alone to complete the work? (DUJAT 2020) 

(a) 90 days (b)225day (c) 145 day (d) 150 days

Solution:

⇒ Work done by one man in one day ⇒ 100/100 = 1%

⇒ work done by 10 men and 15 women in one day = 100/ 6 = 16.67%

⇒ work done by 10 men in one day = 10 x 1 = 10%

⇒ work done by one women in one day = 6.67 / 15 = .44%

⇒ time taken by one woman to do the complete work = 100/ .44 = 225 days.

Hence option B is the correct choice.

Q8. A tap can fill a tank in 48 minutes, whereas another tap can empty it in 2hrs. If both the taps are opened at 11:40 am, then the tank will be filled at

1. 12:40 pm
2. 1:30 pm
3. 1:00 pm
4. 1:00 pm

Solution

⇒ Total volume filled by tap in one hour = 60 / 48 = 1.25 V

⇒ total volume emptied by the tap in one hour = 1/ 2 ⇒ .5V

⇒ net volume filled by the tap in one hour ⇒ 1.25 - .5 ⇒ .75V

⇒ time required to fill the tank = 1 / .75 ⇒ 1.33 hours = 80 minutes

⇒ the tank will be filled at 1:00 pm

Hence option C is the correct choice.

Q9. Pipes A, B and C together can fill a tank in 5hrs. Pipe C is twice as fast as pipe B and pipe B is twice as fast as pipe A. How much time will pipe A alone take to fill the tank.

1. 20 hrs
2. 25 hrs
3. 35 hrs
4. 30 hrs

Solution

⇒ Volume filled by all of them in one hour = ⅕ V

⇒ ratio of a:b:c = 1:2:4, therefore volume filled by A in one hour ⇒ 1/(5 x 7) ⇒ 1/ 35V

⇒ time required by A to fill the whole tank ⇒ 1/volume filled in one hour ⇒ 35 hours

Hence option C is the correct choice.

Q10. There are three taps A,B and C in a tank. They can fill the tank in 10hrs, 20hrs and 25 hrs respectively. At first, all of them are opened simultaneously. Then after 2 hours, tap C is closed and A and B are kept running. After the 4th hour, tap B is also closed. The remaining work is done by tap A alone. Find the percentage of the work done by tap A itself.

1. 32%
2. 67%
3. 72%
4. 82%

Solution

⇒ Work done by all the taps in one hour = 100/10 + 100/20 + 100/25 = 10 + 5 + 4 = 19%

⇒ Work done by Tap C in 2 hours = 2 x 4 = 8%

⇒ work done by tap B in 4 hours = 5 x 4 = 20%

⇒ work done by Tap A = 100 -( 20 + 8 ) = 72%

Hence option C is the correct choice.