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

Work done by P in one day is double the work done by Q in one day and work done by Q in one day is thrice the work done by R in one day. If P, Q and R together can complete the work in 30 days, then in how many days can P alone do the work?

  1. 52 days

  2. 42 days

  3. 30 days

  4. 50 days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let R's work be r. Q = 3r, P = 2Q = 6r. Total work rate = 6r + 3r + r = 10r. They finish in 30 days, so total work = 30 * 10r = 300r. P alone takes 300r / 6r = 50 days.

Multiple choice

A famous bakery in Green hill that remains open from 08:00 am to 08:00 pm is run by two brothers Ian and Johnson. Ian can bake 170 cookies per hour and his brother Johnson can bake 80 cookies per hour. They got an order for 12,000 cookies. Working together, in how many days will both the brothers complete the order?

  1. 2 days

  2. 3 days

  3. 4 days

  4. 5 days

  5. 6 days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Combined rate = 170 + 80 = 250 cookies/hour. Daily capacity = 250 * 12 hours = 3000 cookies/day. Days required = 12000 / 3000 = 4 days.

Multiple choice

Five sowing machines operate at the same constant rate and, working together, can finish sowing the field in 8 days. If the farmer needs to finish sowing the same field in 5 days, how many additional sowing machines will he need to use at the same constant rate?

  1. 2

  2. 3

  3. 4

  4. 5

  5. 6
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total work = 5 machines * 8 days = 40 machine-days. To finish in 5 days, machines needed = 40 / 5 = 8. Additional machines = 8 - 5 = 3.

Multiple choice

Matthew, Noah and Owen can complete a piece of work in 10, 20 and 30 days, respectively. Matthew worked for 5 days and left the job. Then, Noah took up the work, worked for 5 days on it and left. After this, Owen completed the remaining work. If Matthew got $150 for his work, how much amount will Owen get?
  1. $50
  2. $75
  3. $100
  4. $125
  5. $150
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Work rates: M=1/10, N=1/20, O=1/30. M worked 5 days (5/10 = 1/2 work). N worked 5 days (5/20 = 1/4 work). Remaining work = 1 - 1/2 - 1/4 = 1/4. Owen does 1/4 work. Since M got 150 for 1/2 work, 1/4 work is worth 75.

Multiple choice

Directions: Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given, and select one of the following four answer choices: Quantity A Quantity B If 30 people can do a piece of work in 20 days, number of people to complete the work in 4 days If 50 people can do a piece of work in 12 days, number of people to complete the work in 5 days

  1. Quantity A is greater than quantity B.

  2. Quantity B is greater than quantity A.

  3. Both quantities are equal.

  4. The relationship between the quantities cannot be determined.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity A: 30 * 20 = 600 man-days. People needed for 4 days = 600 / 4 = 150. Quantity B: 50 * 12 = 600 man-days. People needed for 5 days = 600 / 5 = 120. 150 > 120, so Quantity A is greater.

Multiple choice

If 9 men working 7.5 hours a day can finish a piece of work in 20 days, then how many days will be taken by 12 men, working 6 hours a day to finish the work? It is being given that 2 men of latter type work as much as 3 men of the former type?

  1. 10.5

  2. 11

  3. 6

  4. 12.5

  5. 13
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The total work is 9 men * 7.5 hours * 20 days = 1350 man-hours. Given 2 men (latter) = 3 men (former), 1 latter man = 1.5 former men. So 12 latter men = 18 former men. Work = 18 * 6 * D = 1350. D = 1350 / 108 = 12.5.

Multiple choice

Abhay can complete a piece of work in 18 days, Balram in 20 days and Chandan in 30 days. Balram and Chandan started the work but were forced to leave after 2 days. How many days will Abhay take to complete the remaining work alone?

  1. 10 days

  2. 12 days

  3. 15 days

  4. 16 days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Balram and Chandan's combined rate = 1/20 + 1/30 = 5/60 = 1/12. In 2 days, they complete 2/12 = 1/6 of the work. Remaining work = 5/6. Abhay's rate = 1/18. Time for Abhay = (5/6) / (1/18) = 15 days.

Multiple choice

The ratio of the capacity to do work of A and B is 3: 2. if they together can complete a work in 18 days, then how long does a take to complete the work alone?

  1. 20 days

  2. 30 days

  3. 45 days

  4. 25 days

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

Since the ratio of the work capacities of A and B is 3:2, we can assume A does 3 units of work per day and B does 2 units. Together they do 5 units of work per day, so the total work is 5 * 18 = 90 units. A alone will take 90 / 3 = 30 days to complete this work.

Multiple choice

A and B can do a work in 10 days and 15 days respectively. If A starts on the work and both work alternatively day after day, in how many days will the work be completed.

  1. 9 days

  2. 10 days

  3. 11 days

  4. 12 days

  5. 14 days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A's daily work = 1/10, B's daily work = 1/15. In a 2-day cycle, they complete 1/10 + 1/15 = 5/30 = 1/6 of the work. In 10 days (5 cycles), they complete 5/6 of the work. On day 11, A does 1/10, total 5/6 + 1/10 = 16/15 (too much). A completes 1/6 of the remaining 1/6 on day 11, and B finishes the rest on day 12.

Multiple choice

A and B can do a bit of work in 12 days. B and C can do it in 15 days while C and A can do it in 20 days. In how long will they complete it cooperating? Additionally, in how long can A alone do it?

  1. 10 days, 30 days.

  2. 15 days, 20 days.

  3. 20 days, 40 days.

  4. 10 days, 50 days.

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

Let rates be A+B=1/12, B+C=1/15, C+A=1/20. Summing these gives 2(A+B+C) = 1/12 + 1/15 + 1/20 = 12/60 = 1/5, so A+B+C = 1/10 (10 days). To find A, subtract B+C: A = 1/10 - 1/15 = 1/30 (30 days).