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

Passage

Directions: Given below are two quantities named I and II. Based on the given information, you have to determine the relation between the two quantities. You are to use the given data and your knowledge of Mathematics to choose among the given options.

Quantity I: 30 workers working 5 hours a day can dig 4/5th of a tunnel in 16 days. Number of days taken by 24 workers working 5 hours a day to dig the remaining tunnel Quantity II: Jack alone can finish printing a book in 12 days and takes 4 days more than Rocky to complete the same task. Both of them printed the book together for 4 days and after that, Jack completed the remaining work along with his friend Joshua in one day. Time taken by Joshua alone to complete 1/2 of the work

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity I < Quantity II

  4. Quantity I = Quantity II or no relation can be established.

  5. Quantity I ≤ Quantity II
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quantity I: 30 workers * 16 days = 480 worker-days for 4/5 of the tunnel. Total work = 600 worker-days. Remaining 1/5 = 120 worker-days. 24 workers * 5 hours = 120 worker-days, so 5 days. Quantity II: Jack = 12 days, Rocky = 8 days. Together = 1/12 + 1/8 = 5/24 per day. In 4 days, they do 20/24 = 5/6. Remaining 1/6 done by Jack and Joshua in 1 day. Joshua's rate = 1/6 - 1/12 = 1/12. Joshua takes 12 days for full work, 6 days for 1/2. Since 5 < 6, Quantity I < Quantity II.

Multiple choice

Passage

Directions: In this problem, a question is given followed by three statements, labelled as A, B and C. Read the statements carefully and determine which of them is/are sufficient/necessary to answer the question.

What is the amount received by a man per week? A. Three men and two women together can do a piece of work in 8 days, and two men and three women together can do the same work in 10 days. B. The men are 250% more efficient than the women. C. Rs. 132 are given to a woman for her contribution towards work.

  1. Only A and C together are sufficient.

  2. Only A and B together are sufficient.

  3. All A, B and C together are necessary.

  4. Either A and C together or B and C together are sufficient.

  5. Only B and C together are sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

Passage

Working alone, Gurmail, using a spade, empties a truckload of sand in 2 hours. Gurtej is 50% more efficient than Gurmail. Gurtej begins emptying a truck on arrival, and after half an hour is joined by Gurmail. A person is paid Rs. 300 to empty a truck.

One day, there were two similar truckloads to be unloaded. That time, Gurmail started the work on the second truck and left after working for 1 hour. Then Gurtej started from where Gurmail left and worked for 40 minutes. How would Gurmail and Gurtej divide the money between themselves if Rs. 400 was paid for this second truck work ?

  1. Rs. 150, Rs. 250

  2. Rs. 250, Rs. 150

  3. Rs. 100, Rs. 300

  4. Rs. 200, Rs. 200
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Gurmail rate = 1 truck/2 hours = 0.5 trucks/hr. Gurtej rate = 1.5 * 0.5 = 0.75 trucks/hr. Second truck: Gurmail works 1 hour (0.5 trucks). Remaining 0.5 trucks done by Gurtej at 0.75 trucks/hr, taking 0.5 / 0.75 = 2/3 hours (40 mins). Total work done: Gurmail 0.5, Gurtej 0.5. Since they did equal work, they split the money equally.

Multiple choice

Passage

Directions to Solve In each of the questions below consists of a question and statements given below it. You have to decide whether the data provided in the statements are sufficient to answer the question.

In how many days B and C together can complete the work? I. Per day efficiency of A, B and C is in the ratio 3 : 2 : 4 II. A and B together can complete the work in 7.2 days III. Time taken by A, B and C alone to complete the work is in the ratio of 4 : 6 : 3.

  1. I and II

  2. II and III

  3. Either I and II or II and III

  4. None is enough

  5. I and III
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

I gives efficiency ratio A:B:C = 3:2:4. II gives A+B work in 7.2 days, so (3+2) * 7.2 = 36 units total work. With I and II, we can find B and C's time. III gives time ratio A:B:C = 4:6:3, which is equivalent to efficiency ratio 3:2:4. Thus, II and III also provide the same information. Both combinations are sufficient.

Multiple choice

Passage

Directions: Study the following information carefully and answer the given question. The data below represents the number of people required for various assignments to be completed in various days. Assignment Situation 1 Situation 2 Number of Employees Days Required Number of Employees Days Required X (p + 10) p (p + 20) (p – 6) Y (q + 5) 60 15 (q + 80) Z 125 r 2 20 s 2

In a group, the total number of employees is (0.2r × 0.5s). Then how many days are required by the group to complete assignment Z?

  1. 500

  2. 450

  3. 550

  4. 600

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

Passage

Directions: Study the following information carefully and answer the given question. The data below represents the number of people required for various assignments to be completed in various days. Assignment Situation 1 Situation 2 Number of Employees Days Required Number of Employees Days Required X (p + 10) p (p + 20) (p – 6) Y (q + 5) 60 15 (q + 80) Z 125 r 2 20 s 2

If (p - 10) employees are working on assignment X, then how many days will it take to complete 1/12th part of assignment X?

  1. 4

  2. 6

  3. 5

  4. 8

  5. 3
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For the same assignment, employees multiplied by days is constant: (p + 10)p = (p + 20)(p - 6), which gives p = 30. The full work is 40 × 30 = 1,200 employee-days, so 1/12 of it requires 100 employee-days, or 100/20 = 5 days.

Multiple choice

Passage

Directions: The data below represents the number of people required for various project to be completed in different number of days. Use this information to answer the question asked. Project Situation I Situation II Number of Workers Number of Days Required Number of Workers Number of Days Required P 1 x (x + 5) (x – 5) (x + 15) P 2 y (y + 10) 40 (y – 5) P 3 50 z 80 (y – 10) P 4 y (z – 1) (x + 10) (z – 4)

If (x – 10) people were working on Project P1, then how many days would it take to complete the work?

  1. 60

  2. 50

  3. 40

  4. 30

  5. 20
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For Project P1, (Workers * Days) is constant. x * (x+5) = (x-5) * (x+15). x^2 + 5x = x^2 + 10x - 75. 5x = 75, so x = 15. If (x-10) = 5 people work, the work is 15 * 20 = 300 man-days. Days = 300 / 5 = 60.

Multiple choice

Passage

Directions: The data below represents the number of people required for various project to be completed in different number of days. Use this information to answer the question asked. Project Situation I Situation II Number of Workers Number of Days Required Number of Workers Number of Days Required P 1 x (x + 5) (x – 5) (x + 15) P 2 y (y + 10) 40 (y – 5) P 3 50 z 80 (y – 10) P 4 y (z – 1) (x + 10) (z – 4)

In a group A, if the total number of workers is (0.2x × 0.8y), then what is the number of days required by group A to complete Project P2, given y > 15?

  1. 12.2

  2. 12

  3. 13

  4. 12.5

  5. 14
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

Passage

Directions: The data below represents the number of people required for various project to be completed in different number of days. Use this information to answer the question asked. Project Situation I Situation II Number of Workers Number of Days Required Number of Workers Number of Days Required P 1 x (x + 5) (x – 5) (x + 15) P 2 y (y + 10) 40 (y – 5) P 3 50 z 80 (y – 10) P 4 y (z – 1) (x + 10) (z – 4)

If 0.4x people work on Project P2 for starting 10 days and then 0.8y people join the project after 10 days, then how many days will it take to complete Project P2, given y < 15?

  1. 30

  2. 20

  3. 25

  4. 40

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

Based on the project data, P2 has y workers and (y+10) days. Total work = y(y+10). With 0.4x workers for 10 days and 0.8y workers for the rest, the equation is 0.4x(10) + 0.8y(days) = y(y+10). Solving with given constraints leads to 20 days.

Multiple choice

Passage

Directions: The data below represents the number of people required for various project to be completed in different number of days. Use this information to answer the question asked. Project Situation I Situation II Number of Workers Number of Days Required Number of Workers Number of Days Required P 1 x (x + 5) (x – 5) (x + 15) P 2 y (y + 10) 40 (y – 5) P 3 50 z 80 (y – 10) P 4 y (z – 1) (x + 10) (z – 4)

In a group B, if the total number of workers is (0.2x × 0.5y × 0.25z), then what is the total number of days required to complete Project P3 by group B, given y > 15?

  1. 4

  2. 21 2

  3. 20 3

  4. 10

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice

Passage

Directions: Study the given information and answer the following question. A firm allots one project to four persons, namely Reema, Suresh, Ramya and Sneha, and they need a certain time to complete the project. Reema alone can complete the whole work in 60 days, while Suresh needs 180 days to complete the whole work alone.

At first, Ramya and Sneha start working together, and together they work for 24 days. After that, they are replaced by Reema and Suresh. The remaining work is completed successfully by Reema and Suresh together in 20 days. The ratio of efficiency of Ramya to that of Sneha is 3 : 5. Find the difference between the times that would be taken by Ramya and Sneha to complete the whole project, working alone.

  1. 14 days

  2. 48 days

  3. 45 days

  4. 36 days

  5. None of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice

Passage

Directions: Read the data carefully and answer the following question. David, John, Mike, and Sam are four workers who together can complete a project 'P' in 9 days and Sam did the one fifth of the project P. The efficiency of David is five times that of Mike, while John's efficiency is 100% more than that of Mike. Also, Mike and David working together can complete the project 'P' in p days, while Mike and Sam working together can complete the project 'P' in y days.

Two workers R and T together can complete an another project 'Q' in (p - 1) days, while T and N together can complete the same work in (y - 18) days. If R, T, and N together can complete project 'Q' in 8 ( p − 1 ) y − 16 days, how much percent is N more efficient as compared to R?

  1. 14 2 7 %

  2. 15%

  3. 25%

  4. 28 4 7 %

  5. 38 3 7 %
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

Passage

Directions: Read the data carefully and answer the following question. David, John, Mike, and Sam are four workers who together can complete a project 'P' in 9 days and Sam did the one fifth of the project P. The efficiency of David is five times that of Mike, while John's efficiency is 100% more than that of Mike. Also, Mike and David working together can complete the project 'P' in p days, while Mike and Sam working together can complete the project 'P' in y days.

If r men can complete the project in (p + 15) days, while (y - 20) men can complete the same work in n days. If (y - 25) men can complete the same project in (n + 9) days, then in how many days can (n - r + 3) men can complete the project?

  1. 9 days

  2. 10 days

  3. 12 days

  4. 18 days

  5. 13 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice

Passage

Directions: Read the data carefully and answer the following question. David, John, Mike, and Sam are four workers who together can complete a project 'P' in 9 days and Sam did the one fifth of the project P. The efficiency of David is five times that of Mike, while John's efficiency is 100% more than that of Mike. Also, Mike and David working together can complete the project 'P' in p days, while Mike and Sam working together can complete the project 'P' in y days.

m men can do a project in n days and n women can do the same project in 3m days. p men and 1.5y women together can complete the same work in 20 days. 5 men and (y + 5) women started working together and they did work only for D days and remaining work is completed by a women in 10D days. Find the value of D.

  1. 28 days

  2. 26 days

  3. 30 days

  4. 34 days

  5. 29 days
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice

Passage

Directions: Read the following information and answer the given question. A, B, C and D are working in a team to complete a project in 5 days. A and B together can complete the work in 10 days, C alone can complete the work in 15 days and A and D together can complete the work in 20 days.

If only A has to complete the whole work, then in how many days will he complete the project?

  1. 50 days

  2. 60 days

  3. 30 days

  4. 40 days

  5. None of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Team (A+B+C+D) = 1/5. C = 1/15. A+B = 1/10. A+D = 1/20. (A+B) + (A+D) + C = 1/10 + 1/20 + 1/15 = (6+3+4)/60 = 13/60. This is A+B+C+D+A = 1/5 + A. 13/60 = 12/60 + A. A = 1/60. Time = 60 days.