Summary: Unlock the key to achieving excellent scores in aptitude exams with remarkable finesse! This article walks through concepts and important questions for "Time and Work Questions for Aptitude Exams 2024"!

The concept of time and work is crucial in all aptitude tests.

Over the past ten years, questions based on this idea have frequently appeared in various aptitude tests, including DUJAT, IPMAT, etc.

On average, you will have 2-3 questions based on this topic every year in the Management Aptitude Entrance examinations.

To ease your preparation, we have compiled important Time and Work Questions for Aptitude Exams 2024 from the previous year's papers and a few self-designed questions by TopRankers faculty.

Download Free Study Material for IPMAT 2024 by SuperGrads

Time and Work Concept Explained with Examples

To solve these questions, first, we need to understand the basic concept of work.

Example 1:

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.

Example 2:

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, 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:

Twenty 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 2024

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.

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

⇒ Total no. of days = 4 days.

Hence option D is the correct choice.

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Q3. A and B required ten 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 complete 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.

Check: IPM Aptitude Questions Based on Remainders

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 ratio 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 on 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.

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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 four units per day

⇒ work done by B will be three units per day

⇒ total work be 8 units per day

⇒ therefore the work done by boys 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)225 dayS (c) 145 dayS (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.

Check: IPM Aptitude Questions Based on Remainders

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.

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11. A group of 8 workers can complete a project in 20 days. If 4 of these workers leave after 8 days, how many more days will it take for the remaining workers to finish the project?

Solution:

The total work to be completed is 8 workers * 20 days = 160 worker-days.

In the first 8 days, the completed work is 8 workers * 8 days = 64 worker-days. The remaining work is 160 worker-days - 64 worker-days = 96 worker-days.

Now, the remaining 4 workers will complete the project in 96 worker-days / 4 workers = 24 days.

12. A machine can print 1200 pages in 6 hours. How many pages can it print in 3 hours?

Solution:

The rate of printing is 1200 pages / 6 hours = 200 pages per hour.

In 3 hours, the machine can print 200 pages/hour * 3 hours = 600 pages.

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13. Two workers can build a wall in 10 days. How many additional workers are needed to complete the same wall in 5 days?

Solution:

The total work to build the wall is 2 workers * 10 days = 20 worker-days.

To complete the wall in 5 days, the required work is 2 workers * 5 days = 10 worker-days.

The additional workers needed are 10 worker-days / 5 days = 2 workers.

14. A contractor hires 12 painters to complete a project in 15 days. After 6 days, 4 painters leave the job. How many more painters should be hired to finish the project on time?

Solution:

The total work to be completed is 12 painters * 15 days = 180 painter-days. In the first 6 days, the completed work is 12 painters * 6 days = 72 painter-days.

The remaining work is 180 painter-days - 72 painter-days = 108 painter-days.

Now, 8 painters are left to complete the project. To finish the remaining work in time, 108 painter-days / 8 painters = 13.5 days.

As we cannot hire half a painter, it's better to round up to 14 days. So, no additional painters are needed.

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15. A factory can produce 3000 units of a product in 12 days. How many units can it produce in 20 days?

Solution:

The rate of production is 3000 units / 12 days = 250 units per day.

In 20 days, the factory can produce 250 units/day * 20 days = 5000 units.

Check: IPM Aptitude Questions & Answers based on Cross Multiplication

How to Prepare for Time and Work Questions for Aptitude Exams 2024?

1. Grasp the Fundamentals: Begin by familiarizing yourself with the basic concepts of time and work. Understand the relationship between time, work done, and the rate of work.
2. Formulas and Shortcuts: Memorize relevant formulas and time-saving shortcuts. These will help you solve problems quickly and efficiently during the exam.
3. Practice Extensively: Practice a wide range of time and work problems, varying in complexity. The more you practice, the better you'll become at identifying patterns and applying the right techniques.
4. Work with Ratios: Learn to work with ratios when dealing with multiple workers or different work rates. Ratios can simplify calculations and lead to quicker solutions.
5. Time Management: During practice sessions, focus on time management. Aim to solve problems within a stipulated time frame to simulate exam conditions.
6. Analyze Mistakes: Review your mistakes and understand where you went wrong. This analysis will help you avoid similar errors in future attempts.
7. Take Mock Tests: Incorporate time and work questions into mock tests. This will give you a sense of the actual exam environment and help refine your exam strategy.

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Conclusion

In conclusion, mastering time and work questions for aptitude exams is a vital skill that empowers individuals to solve complex problems with precision and efficiency. By comprehending the underlying concepts, practising extensively, and employing time-saving techniques, one can confidently approach these questions during exams. Remember, consistency and dedication are key to honing this proficiency, ensuring success and unlocking a world of opportunities in the realm of aptitude assessments. So, embrace the challenge, persist in your efforts, conquer the realm of time and work with unwavering determination. Best of luck on your aptitude exam journey!

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