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

5 men can complete a work in 12 days, 8 women can complete it in 18 days and 10 children can complete the same work in 24 days. In how many days can 10 men, 12 women and 8 children complete the same work?

  1. 3 9/17 days

  2. 4 2/9 days

  3. 5 3/7 days

  4. 6 6/11 days

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

Calculate the work rate: 1 man = 1/60 work/day, 1 woman = 1/144 work/day, 1 child = 1/240 work/day. 10 men + 12 women + 8 children = 10/60 + 12/144 + 8/240 = 1/6 + 1/12 + 1/30 = (10+5+2)/60 = 17/60. Time = 60/17 = 3 9/17 days.

Multiple choice

4 men or 6 women or 9 boys can finish a work in 98 days, and then the number of days taken by 6 men, 4 women and 5 boys to finish the work is?

  1. 28 days

  2. 32 days

  3. 24 days

  4. 36 days

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

4M = 6W = 9B = 1 unit of work in 98 days. Thus, 1M = 98/4, 1W = 98/6, 1B = 98/9 units per day. The combined rate of 6M + 4W + 5B is 6(1/98*4) + 4(1/98*6) + 5(1/98*9) = (6/4 + 4/6 + 5/9)/98 = (54+24+20)/(36*98) = 98/(36*98) = 1/36. The work is finished in 36 days.

Multiple choice

A and B alone can do a piece of work in x and (x + 10) days respectively and they work together can finish the work in 9 3/8 days. Then find the efficiency ratio of A and B?

  1. 2:7

  2. 5:3

  3. 2:3

  4. 1:3

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

A takes x days, B takes x+10 days. Together they take 75/8 days. 1/x + 1/(x+10) = 8/75. (2x+10)/(x^2+10x) = 8/75. 150x + 750 = 8x^2 + 80x. 8x^2 - 70x - 750 = 0. 4x^2 - 35x - 375 = 0. Solving gives x = 15. A takes 15 days, B takes 25 days. Efficiency ratio is inverse of time ratio: 25:15 = 5:3.

Multiple choice

If Rob, Noah and Fellora work alone, then they are able to complete a piece of work in 9 days, 14 days and 18 days, respectively. If all three of them work together to complete the work and earn the income as the 15th multiple of the second-highest factor of 1,045, then what is the sum of shares of Noah and Fellora?
  1. $1,547
  2. $1,672
  3. $1,768
  4. $1,824
  5. $1,963
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Work rates: Rob=1/9, Noah=1/14, Fellora=1/18. Total rate = (14+9+7)/126 = 30/126 = 5/21. The factors of 1045 are 1, 5, 11, 19, 55, 95, 209, 1045. Second-highest factor is 209. 15th multiple is 209 * 15 = 3135. Noah and Fellora's share is proportional to their rates: (1/14 + 1/18) / (5/21) = (16/126) / (30/126) = 16/30 = 8/15. Share = 3135 * (8/15) = 1672.

Multiple choice

Jimmy can build a wall in 80 days. Bella can build the same wall in 30 days and Sam can build it in 24 days. They all started building the wall together alternately where Jimmy built the wall on the 1st day, then Bella built it on the 2nd day, then Sam on the 3rd day and so on. They kept on working like that till the wall was complete. If they got a total of $6,000, how much would Sam get from it?
  1. $2,750
  2. $2,800
  3. $2,850
  4. $2,900
  5. $2,950
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

Tia, Lany and Marcus loaded a huge truck with paper products. The hourly wages were the same for all the three. They got a total of $210. If Tia worked for 3 hours, Lany worked for 6 hours and Marcus worked for 5 hours, how much did Tia get if they got the money in proportion to the number of hours they worked for?
  1. $35
  2. $43
  3. $45
  4. $50
  5. $60
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total hours = 3 + 6 + 5 = 14. Tia's share = (3/14) * 210 = 3 * 15 = 45.

Multiple choice

The ratio of efficiency of P is to R is 7 : 4 and the ratio of number of days taken by Q is to R is 2 : 3 while working alone P takes 9 days less than R to complete the work. If Q and R started the work and left after 2 days then find the number of days taken by P to finish the remaining work?

  1. 64/7 days

  2. 8 days

  3. 32/1 days

  4. 128/7 days

  5. 7 days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Efficiency P:R = 7:4. Days Q:R = 2:3 => Efficiency Q:R = 3:2 = 6:4. So P:Q:R = 7:6:4. Let P=7x, Q=6x, R=4x. P takes 9 days less than R: 1/4x - 1/7x = 9/W => 3/28x = 9/W => W = 84x. P takes 84x/7x = 12 days. R takes 84x/4x = 21 days. Q takes 84x/6x = 14 days. Q+R work 2 days: (1/14 + 1/21)*2 = (3+2)/42 * 2 = 10/42 = 5/21. Remaining = 16/21. P finishes in (16/21) * 12 = 192/21 = 64/7 days.

Multiple choice

How many days A, B and C can complete the work together? Statement I – Ratio of efficiency of A and B is 2:1. B and C can complete the work in 12 days. Statement II – Ratio of efficiency of A and C is 3:1. C can alone complete the work in 30 days.

  1. Only Statement I alone

  2. Only Statement II alone.

  3. Both Statements I and II together.

  4. Neither Statement I nor II is sufficient.

  5. Either Statement I or II.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement I gives the ratio of A:B and the combined rate of B+C. Statement II gives the ratio of A:C and the rate of C. Together, these provide enough information to determine the individual efficiencies of A, B, and C, allowing the calculation of their combined work time.

Multiple choice

L and M together can complete a piece of work in 72 days, M and N together can complete it in 120 days, and L and N together in 90 days. In what time can L alone complete the work?

  1. 150 days

  2. 80 days

  3. 100 days

  4. 120 days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

1/L + 1/M = 1/72, 1/M + 1/N = 1/120, 1/L + 1/N = 1/90. Sum = 2(1/L + 1/M + 1/N) = 1/72 + 1/120 + 1/90 = (5+3+4)/360 = 12/360 = 1/30. 1/L + 1/M + 1/N = 1/60. 1/L = 1/60 - 1/120 = 1/120. L = 120 days.

Multiple choice

30 men can complete a job in 40 days. However, after 24 days some men out of the assigned 30 left the job. The remaining people took another 40 days to complete the job. The number of men who left the job is

  1. 24

  2. 18

  3. 12

  4. 6
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total work is 30 men * 40 days = 1200 man-days. In 24 days, 30 men did 30 * 24 = 720 man-days of work, leaving 480 man-days. Since the remaining work took 40 days, the number of men left is 480 / 40 = 12 men. Thus, 30 - 12 = 18 men left the job.