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' alone can do a piece of work in 24 days. If his friend 'B' joins him for the first 4 days, the work is finished in 6 days less. How many days will B alone take to do the work?

  1. 12 days

  2. 15 days

  3. 16 days

  4. 18 days

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

A does the work in 24 days, so A's rate is 1/24 per day. The work is finished in 24 - 6 = 18 days. In 18 days, A does 18/24 = 3/4 of the work. B must have done the remaining 1/4 of the work in the first 4 days. B's rate is (1/4) / 4 = 1/16, so B takes 16 days.

Multiple choice

Directions: A and B can do a piece of work in 20 and 30 days, respectively. A, B and C worked together to complete the work. They got \$900 for completing the work. If they shared the money according to the work done by them, B would get \$150 more than the amount C gets. How much money will A get?
  1. $300
  2. $450
  3. $500
  4. $600
  5. $800
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A's work rate is 1/20, B's is 1/30. Let C's rate be 1/x. Total work = 1. The ratio of their shares is proportional to their work rates. Solving the system based on the total 900 and the difference between B and C leads to A receiving 450.

Multiple choice

On nth day, n persons work (where n = 1, 2, 3, …..). This means that on first day, only one person works; on second day, 2 persons work, and so on. If the work is completed in 25 days, how many days does it take to complete the same work by a team of 25 people, if they work regularly?

  1. 9

  2. 13

  3. 12

  4. 15

  5. 16
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total work = sum of 1+2+3+...+25 = (25 * 26) / 2 = 325 person-days. If 25 people work regularly, time = 325 / 25 = 13 days.

Multiple choice

A and B together can do a piece of work in 20 days, whereas B and C together can do the same piece of work in 30 days. How many days will A and C together take to complete the same piece of work?

  1. 10 days

  2. 24 days

  3. 25 days

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

Let A, B, C be the work rates. A + B = 1/20 and B + C = 1/30. We want A + C. Subtracting the equations gives A - C = 1/20 - 1/30 = 1/60. We cannot determine A + C without knowing the individual rates or another relation.

Multiple choice

Bob and Smith together can finish a piece of work in 8 days. Both start the work together. After 3 days, Bob falls ill. Smith alone finishes the remaining work in 15 days. How many days would Bob take working alone to finish that work?

  1. 10 days

  2. 11 days

  3. 12 days

  4. 15 days

  5. 18 days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Together rate = 1/8. In 3 days, they do 3/8 of work. Remaining = 5/8. Smith does 5/8 in 15 days, so Smith's rate = (5/8)/15 = 1/24. Bob's rate = 1/8 - 1/24 = 3/24 - 1/24 = 2/24 = 1/12. Bob takes 12 days.

Multiple choice

If 2 boys and 5 girls complete a piece of work in 3 days, while 6 boys and 6 girls complete the same work in 2 days, then how many days will 1 girl alone take to finish the work?

  1. 36 days

  2. 18 days

  3. 12 days

  4. 10 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let B be the work done by a boy per day and G be the work done by a girl per day. We have 2B + 5G = 1/3 and 6B + 6G = 1/2. Multiplying the first equation by 3 gives 6B + 15G = 1. Subtracting the second equation (6B + 6G = 1/2) from this gives 9G = 1/2, so G = 1/18. One girl takes 18 days.

Multiple choice

In a Bilaspur village, 12 men and 18 boys completed construction of a primary health centre in 60 days, by working for 7.5 hours a day. Subsequently, the residents of the neighbouring Harigarh village also decided to construct a primary health centre in their locality, which would be twice the size of the centre built in Bilaspur. If a man is able to perform the work equal to the same done by 2 boys, then how many boys will be needed to help 21 men to complete the work in Harigarh village in 50 days, working for 9 hours a day?

  1. 45

  2. 48

  3. 40

  4. 42
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Work = Men * Days * Hours. 1 man = 2 boys. 12 men + 18 boys = 24 boys + 18 boys = 42 boys. Work1 = 42 * 60 * 7.5 = 18900 boy-hours. Work2 = 2 * Work1 = 37800 boy-hours. 21 men + x boys = 42 boys + x boys = (42+x) boys. Work2 = (42+x) * 50 * 9 = 37800. 42+x = 37800 / 450 = 84. x = 42.

Multiple choice

30 men can finish a piece of work in 10 days, whereas it takes 12 women to finish it in 10 days. If 15 men and 6 women undertake to complete the same work, how many days will they take to complete the work?

  1. 20

  2. 15

  3. 12

  4. 10

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

30 men = 10 days, so 1 man = 300 man-days. 12 women = 10 days, so 1 woman = 120 woman-days. 15 men = 15/300 = 1/20 of work per day. 6 women = 6/120 = 1/20 of work per day. Combined rate = 1/20 + 1/20 = 2/20 = 1/10. Time = 10 days.

Multiple choice

It was expected that 10 men together would complete a piece of work in 40 days. But after a few days, they increased their efficiency by 25% and completed the work six days earlier. How many days after the start of the work did they increase their efficiency?

  1. 5

  2. 6

  3. 8

  4. 10

  5. 12
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let x be the days worked at normal efficiency. Total work = 10 * 40 = 400 man-days. After x days, 10x work is done. Remaining work = 400 - 10x. Efficiency increases by 25%, so new rate is 12.5 men. They finish in (40 - x - 6) = 34 - x days. Equation: 10x + 12.5(34 - x) = 400. 10x + 425 - 12.5x = 400. 2.5x = 25, so x = 10.