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

Working at 20% more efficiency, A can complete a work in 3 days less, whereas, working at 11⅑% more efficiency, A and B together can complete the same work in 1 day less. If A, B and C, working together, can complete the same work in 6 days, and they are paid a total of ₹33,000 for the completion of the work, what'll be the share of C in it?

  1. ₹13,200

  2. ₹16,500

  3. ₹14,400

  4. None of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let A's efficiency be a. 1.2a * (T-3) = a * T -> 1.2T - 3.6 = T -> 0.2T = 3.6 -> T = 18 days. A's rate = 1/18. A+B together at 11.11% (1/9) more efficiency: (1+1/9) * (A+B) * (T-1) = 1. (10/9) * (A+B) * 17 = 1. (A+B) = 9/170. B = 9/170 - 1/18 = (81-85)/1530 = -4/1530. This implies the problem constraints are inconsistent.

Multiple choice

The amount of work that five boys and one man can complete in a day, and the work that two women and two men can complete in a day, are 50% and 66⅔%, respectively of the total work that three women, four boys and two men can complete in a day. Two women, three boys and two men can complete what percentage of the work in a day?

  1. 80%

  2. 83.33%

  3. 87.5%

  4. 78%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let W, B, M be daily work of woman, boy, man. 5B + M = 0.5(3W + 4B + 2M) => 10B + 2M = 3W + 4B + 2M => 3W = 6B => W = 2B. 2W + 2M = (2/3)(3W + 4B + 2M) => 6W + 6M = 6W + 8B + 4M => 2M = 8B => M = 4B. Target: 2W + 3B + 2M = 2(2B) + 3B + 2(4B) = 4B + 3B + 8B = 15B. Total work = 3W + 4B + 2M = 3(2B) + 4B + 2(4B) = 6B + 4B + 8B = 18B. Percentage = 15/18 = 5/6 = 83.33%.

Multiple choice

240 men started working on a project which is supposed to be completed in 10 days. But starting from the second day, two men left the project every day till the 10th day. What is the percent of work which will be left undone after 10 days?

  1. 2.5%

  2. 3.25%

  3. 2.75%

  4. 3.75%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total work = 240 * 10 = 2400 man-days. Work done: Day 1 = 240, Day 2 = 238, ..., Day 10 = 222. This is an arithmetic progression with 10 terms. Sum = (10/2) * (240 + 222) = 5 * 462 = 2310. Work left = 2400 - 2310 = 90. Percent left = (90 / 2400) * 100 = 3.75%.

Multiple choice

Usually, when Ajay and Vinod each work for 8 hours a day, they take 10 days to complete a job, working together. When Ajay works at 75% of his efficiency and Vinod works at 125% of his efficiency, they take 9 days to complete the same job, working together. What will be the time taken by them to complete the job if Ajay works at 125% of his efficiency and Vinod works at 75% of his efficiency?

  1. 12 days

  2. 12.75 days

  3. 11.25 days

  4. 11 days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let A and V be the efficiencies. (A+V)*8*10 = Work. (0.75A + 1.25V)*8*9 = Work. Solving these gives A = V. Then (1.25A + 0.75A)*8*T = Work. T = 80/1.6 = 11.25 days.

Multiple choice

Geeta, Mina and Sunita, working together, take 4 days to finish a job. Instead, if only Geeta and Sunita take up the job, they can finish it in 15 days less than the time taken by Mina to complete the job, working alone. Mina started the job and after 2 days Geeta and Sunita joined her. Mina quit after working for 2 more days. In how many days was the job completed?

  1. 5

  2. 6

  3. 7

  4. 8
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let M be the time for Mina. G+S+M = 1/4. G+S = 1/(M-15). So 1/(M-15) + 1/M = 1/4. Solving M^2 - 23M + 60 = 0 gives M=20 or M=3. Since M>15, M=20. G+S = 1/5. Mina works 4 days (2+2), G+S work 2 days. Work done = 4/20 + 2/5 = 1/5 + 2/5 = 3/5. Remaining 2/5 work done by G+S in (2/5) / (1/5) = 2 days. Total time = 4 + 2 = 6 days.

Multiple choice

The efficiencies of A, B and C are in harmonic progression with distinct terms. If C works at double of his efficiency, then the number of days taken by A and C to complete a work, working together, will be one-third the number of days taken by B alone to complete the work. In how many days can A alone complete the work?

  1. 2

  2. 4

  3. 3

  4. Cannot be determined
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the efficiencies be 1/x, 1/y, 1/z in harmonic progression. The problem provides insufficient constraints to uniquely determine the individual efficiencies or the time taken by A alone, as the harmonic progression condition and the work-rate equation do not yield a unique solution for the variables.

Multiple choice

When A and B collaborate only with C, the number of days they would take to complete a project, working together, would be 12.5% more than what they would take when they collaborate only with D who is twice as efficient as C. If A and B decided to collaborate with both C and D, then the number of days they would take to complete the project will be what percentage less than the number of days they would have taken to complete it had they collaborated only with C?

  1. 25

  2. 20

  3. 30

  4. 15
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

Sam can complete a job in 20 days when working alone. Mohit is twice as fast as Sam and thrice as fast as Ayna in the same job. The undertake a job with an arrangement where Sam and Mohit work together on the first day, Sam and Ayna on the second day, Mohit and Ayna on the third day, and this three-day pattern is repeated till the work gets completed. Then, the fraction of total work done by Sam is

  1. 3 20

  2. 3 10

  3. 1 5

  4. 1 20
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Sam rate = 1/20. Mohit rate = 2/20 = 1/10. Ayna rate = (1/10)/3 = 1/30. In 3 days: (S+M) + (S+A) + (M+A) = 2(S+M+A) = 2(1/20 + 1/10 + 1/30) = 2(6/60 + 3/60 + 2/60) = 2(11/60) = 11/30. Sam works on day 1 and 2, total 2/20 = 1/10. The pattern repeats. Total work = 1. The fraction is 3/10.

Multiple choice

A farmer earns Rs. Q per hour for working in his field. For every hour he works beyond S hours in a day, he is paid 2.5 times his regular hourly rate. On one particular day, he works for M hours and earns Rs. 1,800 more than his usual daily income. If Q is either 80 or 120, what are the possible values of M and S? (i) 14, 8 (ii) 16, 9 (iii) 18, 12 (iv) 20, 16 (v) 14, 5

  1. Only (i) and (iii)

  2. Only (ii) and (iv)

  3. Only (ii) and (v)

  4. Only (i), (iii) and (v)

  5. All of the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

D, E, and F can complete a project in 30 days, 24 days, and 20 days respectively. If D and F work together for y days and E completes the remaining work alone in 4y days, then find the value of 2y.

  1. 8

  2. 10

  3. 12

  4. 6

  5. 4
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Rates are D=1/30, E=1/24, F=1/20. Work done by D and F in y days is y(1/30 + 1/20) = y(5/60) = y/12. Remaining work is 1 - y/12. E completes this in 4y days: 4y(1/24) = 1 - y/12. So y/6 = 1 - y/12, which means 3y/12 = 1, so y = 4. Thus 2y = 8.

Multiple choice

One morning, Aditi began designing a project at 8 AM, and Bhavna joined her 3 hours later. They worked together and completed the project at 8 PM the same day. Had they both started working together at 8 AM, the project would have been finished 1.5 hours earlier. Working alone, the time Aditi would take to complete the entire project, in hours, is:

  1. 15

  2. 19

  3. 21

  4. 23
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let A and B be the rates of Aditi and Bhavna. Total time from 8 AM to 8 PM is 12 hours. Aditi works 12 hours, Bhavna works 9 hours. 12A + 9B = 1 (project). If they started together, they finish in 10.5 hours: 10.5(A+B) = 1. Solving the system: 12A + 9B = 1 and 10.5A + 10.5B = 1. From second, B = 1/10.5 - A. Substitute into first: 12A + 9(1/10.5 - A) = 1 => 3A = 1 - 9/10.5 = 1.5/10.5 = 1/7. A = 1/21. Aditi takes 21 hours.

Multiple choice

Ayesha, Rohan, and Kabir are assigned a painting project. Ayesha can complete the project alone in 30 days, Rohan in 24 days, and Kabir in 40 days. Rohan works on the project daily. Ayesha works only on alternate days beginning from Day 1, while Kabir assists only on alternate days starting from Day 2. On which day will the project be completed?

  1. 12th day

  2. 13th day

  3. 14th day

  4. 15th day
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Ayesha rate = 1/30, Rohan = 1/24, Kabir = 1/40. Day 1: A+R = 1/30 + 1/24 = 9/120 = 3/40. Day 2: R+K = 1/24 + 1/40 = 8/120 = 1/15. Cycle of 2 days = 3/40 + 1/15 = 17/120. In 14 days (7 cycles), work done = 7 * 17/120 = 119/120. Remaining 1/120 on Day 15 by A+R, which is enough.