Quantitative Aptitude

Time and Work

2,195 Questions
All Pairwise rates and staged schedules 440 Workers-days-hours chain rule 439 LCM units and efficiency ratios 409 Different worker categories 311 Combined rates and an unknown worker 257 Division of wages 219 Alternate work 110 Opposing rates 10

Time and Work Questions

Multiple choice

A group of researchers started a data analysis project. On the first day, one researcher began the work. Each subsequent day, one additional researcher joined the project. This pattern continued until the project was completed in 20 days. If the efficiency of each researcher is the same, how many days would it take for a team of 14 researchers, working regularly, to complete the same project?

  1. 9

  2. 15

  3. 18

  4. 24
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The total work is the sum of researchers working each day: 1+2+3+...+20 = (20 * 21) / 2 = 210 man-days. If 14 researchers work every day, the time taken is 210 / 14 = 15 days.

Multiple choice

A team of 15 technicians was assigned to complete a network installation project in 45 days. However, after a certain number of days, they increased their working efficiency by 20% and finished the project five days ahead of schedule. How many days after starting the project did they increase their efficiency?

  1. 10 days

  2. 12 days

  3. 15 days

  4. 18 days

  5. 21 days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The total work is 15 technicians * 45 days = 675 man-days. Let x be the days worked at normal efficiency. The remaining (45 - x) days were finished in (45 - 5 - x) = (40 - x) days at 1.2 efficiency. Thus, 15x + 15 * 1.2 * (40 - x) = 675. Solving for x gives 15x + 18(40 - x) = 675, so 15x + 720 - 18x = 675, which leads to 3x = 45, or x = 15.

Multiple choice

At a manufacturing plant, a team of 4 engineers and 9 robots can complete a project in half the time it takes for a team of 4 robots and 7 engineers to finish the same project. Additionally, it is known that 3 robots can complete the project in 15 days. How many engineers working at the same pace can finish the same project in 15 days?

  1. 15

  2. 21

  3. 24

  4. 30

  5. a
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let R be the rate of a robot and E be the rate of an engineer. 3R = 1/15 project/day, so R = 1/45. The work equation (4E + 9R) * T = (4R + 7E) * 2T implies 4E + 9R = 8R + 14E, so R = 10E. Since R = 1/45, E = 1/450. To finish in 15 days, we need 1/15 / (1/450) = 30 engineers.

Multiple choice

Ankit is thrice as good a workman as Babu and is able to finish a job in 60 days less than Babu. If Ankit and Babu completes 2/3 part of the job and Ankit is replaced by Vivek, then the remaining job is done by Babu and Vivek in 10 days. If Ankit and Babu completes 3/4 part of the job and Babu is replaced by Rahul, the remaining job is done by Ankit and Rahul in 5 days. How long will it take for Ankit, Babu, Vivek and Rahul to complete the job if they work together?

  1. 10 days

  2. 15 days

  3. 8 days

  4. 12 days

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let Ankit's rate be 3x and Babu's rate be x. Since Ankit takes 60 days less, 1/x - 1/3x = 60, so 2/3x = 60, x = 1/90. Babu takes 90 days, Ankit takes 30 days. Solving the work equations for Vivek and Rahul leads to their individual rates. Calculating the combined rate of all four yields 1/12, meaning 12 days.

Multiple choice

During a community project, Alice and Bob were assigned to paint a mural. Alice can paint 1 3 of the mural in 6 days, and Bob can paint 1 4 of the same mural in 5 days. Quantity A: Number of days it would take for both to finish painting the mural, working together Quantity B: 10 days

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be determined from the information given
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Alice paints 1/3 of the mural in 6 days, so she paints 1/18 per day. Bob paints 1/4 in 5 days, so he paints 1/20 per day. Together, they paint (1/18 + 1/20) = (10/180 + 9/180) = 19/180 per day. The time taken is 180/19 days, which is approximately 9.47 days. Since 9.47 < 10, Quantity B is greater.

Multiple choice

Dinesh alone can do a piece of work in 6 days while Sachin alone can do the same piece of work in 12 days. They both start working together. If Sachin leaves when half of the work is done, then how many more days will Dinesh take to complete the remaining work?

  1. 2

  2. 3

  3. 4

  4. 5

  5. 8
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Dinesh's rate is 1/6 work/day and Sachin's is 1/12 work/day. Together, their rate is 1/6 + 1/12 = 3/12 = 1/4 work/day. They complete half the work (1/2) in (1/2) / (1/4) = 2 days. The remaining 1/2 work is done by Dinesh alone at 1/6 rate, taking (1/2) / (1/6) = 3 days.

Multiple choice

Directions: In the following item, Quantity I and Quantity II are given. Determine the relationship between the quantities and choose the appropriate option. Quantity I: The number of days it takes for 5 workers to complete a task if 3 workers can complete the same task in 12 days. Quantity II: The number of days it takes for 7 workers to complete a task if 4 workers can complete the same task in 14 days.

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≥ Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II, or No relation
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Quantity I: 3 workers * 12 days = 36 worker-days. 36 / 5 = 7.2 days. Quantity II: 4 workers * 14 days = 56 worker-days. 56 / 7 = 8 days. 7.2 < 8, so I < II.

Multiple choice

A workshop has three workers: A, B, and C. A can complete a task in 20 days, B can complete it in 25 days, and C can complete it in 30 days. If A and B work together for 10 days, and then C alone finishes the task, how many days does C take to complete the remaining work?

  1. 3 days

  2. 4 days

  3. 6 days

  4. 7 days

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A's rate is 1/20 and B's rate is 1/25. In 10 days, they complete 10 * (1/20 + 1/25) = 10 * (5/100 + 4/100) = 10 * (9/100) = 0.9 of the task. The remaining 0.1 of the task is completed by C, whose rate is 1/30; thus, C takes 0.1 / (1/30) = 3 days.

Multiple choice

A crew of workers is tasked with repairing a road. If all work together, they can complete the job in 12 days. If half of the crew works for the first 8 days, and the remaining half joins them afterward, how many more days will it take to complete the job?

  1. 5 days

  2. 6 days

  3. 7 days

  4. 8 days

  5. 9 days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the total work be 12 units (1 unit/day). Half crew (0.5 units/day) works for 8 days, completing 4 units. Remaining work is 8 units. Now the full crew (1 unit/day) works, taking 8/1 = 8 days.

Multiple choice

Two workers, A and B, work on a project together for the first 5 days. Worker A can complete the project in 10 days, while Worker B can do it in 15 days. After 5 days, Worker A leaves, and Worker B completes the remaining work alone. Quantity A The total number of days taken to complete the project Quantity B 7 days

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be determined from the information given.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A does 1/10 of the work per day, B does 1/15. Together, they do (1/10 + 1/15) = 5/30 = 1/6 of the work per day. In 5 days, they complete 5/6 of the work, leaving 1/6 for B. B takes (1/6) / (1/15) = 2.5 days to finish. Total time = 5 + 2.5 = 7.5 days, which is greater than 7.

Multiple choice

A builder appoints three construction workers Akash, Sunil and Rakesh on one ofhis sites. They take 20, 30 and 60 days respectively to do a piece of work. How manydays will it take Akash to complete the entire work if he is assisted by Sunil and Rakeshevery third day?

  1. 10 days

  2. 15 days

  3. 25 days

  4. 30 days

  5. 45 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Akash works at a rate of 1/20 per day. Every third day, Sunil (1/30) and Rakesh (1/60) help, making the combined rate 1/20 + 1/30 + 1/60 = 6/60 = 1/10. In a 3-day cycle, Akash works alone for 2 days (2/20 = 1/10) and with help for 1 day (1/10), totaling 2/10 = 1/5 of the work per cycle. Thus, 5 cycles (15 days) are needed to complete the work.

Multiple choice

To complete a piece of work, Samir takes 6 days and Tanvir takes 8 days alonerespectively. Samir and Tanvir took Rs.2400 to do this work. When Amir joined them,the work was done in 3 days. What amount was paid to Amir?

  1. Rs. 300

  2. Rs. 400

  3. Rs. 800

  4. Rs. 500

  5. Rs. 100
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Samir's rate is 1/6 and Tanvir's is 1/8. Together with Amir, they complete the work in 3 days, so their combined rate is 1/3. Amir's rate is 1/3 - (1/6 + 1/8) = 1/3 - 7/24 = 1/24. Amir's share of the 2400 is (1/24) / (1/3) * 2400 = (1/8) * 2400 = 300.