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 can do a piece of work in 15 days. B is 25% more efficient than A and C is 40% more efficient than B. A and C work together for 3 days and then C leaves. A and B together will complete the remaining work in:
  1. $2.5$
  2. $3$
  3. $3.5$
  4. $4$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A's rate is 1/15 work/day. B is 25% more efficient, so B's rate is 1.25 × (1/15) = 1/12 work/day. C is 40% more efficient than B, so C's rate is 1.4 × (1/12) = 7/60 work/day. A and C together for 3 days complete 3 × (1/15 + 7/60) = 33/60 work. Remaining work is 27/60. A and B together have rate 1/15 + 1/12 = 9/60. Time needed is (27/60)/(9/60) = 3 days.

Multiple choice

Ram and Shyam together can do a work in 8 days. Both of them began to work. After 3 days Ram fell ill. Shyam completed the remaining work in 15 days. In how many days can Ram complete the whole work?

  1. 17

  2. 12

  3. 15

  4. 13
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Ram and Shyam together complete work in 8 days, so their combined rate is 1/8 per day. After 3 days, 3/8 work is done, leaving 5/8. Shyam completes 5/8 in 15 days, so Shyam's rate = (5/8)/15 = 1/24 per day. Ram's rate = Combined rate - Shyam's rate = 1/8 - 1/24 = 3/24 - 1/24 = 2/24 = 1/12 per day. Therefore, Ram alone completes the work in 12 days. Options A (17), C (15), and D (13) are incorrect.

Multiple choice

Samir and Puneet can complete the same work in 10 days and 15 days respectively. The work was assigned for Rs.4500. After working together for 3 days Samir and Puneet involved Ashok. The work was completed in total 5 days. What amount (in Rs.) was paid to Ashok?

  1. 1500

  2. 800

  3. 750

  4. 542
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Samir's 1-day work = 1/10, Puneet's 1-day work = 1/15. Together in 3 days, they complete: 3 × (1/10 + 1/15) = 3 × (1/6) = 1/2 of work. Remaining work = 1/2. Ashok worked for 2 days (total 5 days - 3 days already done) to complete the remaining half. So Ashok's 2-day work = 1/2, meaning Ashok's 1-day work = 1/4. Wages distributed proportionally to work done: Samir gets 5/10 × 4500 = 2250, Puneet gets 5/15 × 4500 = 1500, Ashok gets 2/4 × 4500 = 750.

Multiple choice

A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 4 days B had to leave. Then A working with a new worker C completed the remaining work in 3 days. If C works alone, in how many days he can do 40% of the same work?

  1. 9

  2. 10

  3. 8

  4. 8.5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A's 1 day work = 1/15, B's = 1/10. In 4 days together: 4(1/15+1/10) = 4(5/30) = 2/3. Remaining = 1/3. A + C do 1/3 in 3 days, so (1/15 + 1/C) × 3 = 1/3, giving 1/C = 2/45. C alone does full work in 22.5 days. 40% of work = 0.4 × 22.5 = 9 days. The key is finding C's rate from the combined work rate.

Multiple choice

Each one of five men independently can complete a work in 20 days. The work is started by one person. Next day one more person joins and every next day one more person joins. From the fifth day, five persons continued working as a team. In how many days, will the work be completed?

  1. 3

  2. 5

  3. 2

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

Each person can do 1/20 of the work per day. Day 1: 1 person completes 1/20. Day 2: 2 persons complete 2/20. Day 3: 3 persons complete 3/20. Day 4: 4 persons complete 4/20. After 4 days, total done = 10/20 = 1/2. Remaining 1/2 is done by 5 persons at 5/20 per day, taking 2 more days. Total = 6 days.

Multiple choice

A can do a certain work in 15 days. B is 25% more efficient than A. Both worked together for 4 days. C alone completed the remaining work in 8 days. A, B and C together will complete the same work in?

  1. 5 days

  2. 6 days

  3. 4 days

  4. 7 days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A's work rate = 1/15 per day. B is 25% more efficient, so B's rate = 1.25 × 1/15 = 1/12 per day. In 4 days, A+B complete 4×(1/15+1/12) = 3/5 of work. Remaining 2/5 is done by C in 8 days, so C's rate = (2/5)/8 = 1/20 per day. Combined rate = 1/15+1/12+1/20 = 1/5, so time = 5 days.

Multiple choice

Two men and 7 women can complete a work in 28 days whereas 6 men and 16 women can do the same work in 11 days. In how many days can 7 men complete the same work?

  1. 22

  2. 20

  3. 18

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

Let one man's daily work = m and one woman's daily work = w. From given: (2m+7w)×28 = 1 and (6m+16w)×11 = 1. Solving simultaneously gives m = 1/154 and w = 1/308. For 7 men: combined rate = 7×(1/154) = 1/22 per day, so time = 22 days.

Multiple choice

A and B can complete a certain work in 6 days and 8 days, respectively. They worked together for 3 days. C alone completed the remaining work in 2 days. B and C together can complete (\frac{3}{4}) of the same work in:

  1. 6 days

  2. 4 days

  3. 3 days

  4. 2 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A's rate = 1/6 work per day, B's rate = 1/8 work per day. Combined A+B rate = 1/6 + 1/8 = 7/24 per day. In 3 days together they complete 3 × 7/24 = 7/8 work. Remaining work = 1 - 7/8 = 1/8. C completes 1/8 work in 2 days, so C's rate = 1/16 per day. B+C combined rate = 1/8 + 1/16 = 3/16 per day. Time to complete 3/4 work = (3/4) / (3/16) = 4 days.

Multiple choice

A, B and C can complete a work in (x), 30 and 45 days, respectively. B and C worked together for 6 days. The remaining work was completed by A alone in 12 days. The value of (x) is:

  1. 24

  2. 20

  3. 18

  4. 15
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Work rates: A = 1/x, B = 1/30, C = 1/45 work per day. B and C together: 1/30 + 1/45 = 5/90 = 1/18 per day. In 6 days, B+C complete 6/18 = 1/3 of work. Remaining 2/3 is done by A in 12 days, so A's rate = (2/3)/12 = 1/18. Since A = 1/x, we have 1/x = 1/18, so x = 18 days.

Multiple choice

A and B together can complete a certain work in 20 days whereas B and C together can complete it in 24 days. If A is twice as good a workman as C, then in what time will B alone do 40% of the same work?

  1. 12 days

  2. 10 days

  3. 18 days

  4. 15 days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let A, B, C be work rates (work per day). A + B = 1/20 and B + C = 1/24. Given A = 2C. Substituting: 2C + B = 1/20 and B + C = 1/24. Subtracting: C = 1/20 - 1/24 = (6-5)/120 = 1/80. So A = 2/80 = 1/40 and B = 1/24 - 1/80 = (10-3)/240 = 7/240. Wait, let me verify: from B + 1/80 = 1/24, B = 1/24 - 1/80 = (10-3)/240 = 7/240. For 40% work: B needs 0.40/(7/240) = 96/7 days. Hmm, let me recheck the calculation. Actually, from the given: A + B = 1/20 and A = 2C, so 2C + B = 1/20. Also B + C = 1/24. From these, C = 1/20 - 1/24 + C... wait. Subtracting: (2C + B) - (B + C) = 1/20 - 1/24, so C = 1/120. Then A = 1/60, and B = 1/24 - 1/120 = 4/120 = 1/30. For 40% work by B alone: 0.40/(1/30) = 12 days.

Multiple choice

A and B can do a piece of work in 18 days. B and C together can do it in 30 days. If A is twice as good a workman as C, find in how many days B alone can do the work?

  1. 90 days

  2. 80 days

  3. 75 days

  4. 100 days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A is twice as efficient as C, so if C's rate is c, A's rate is 2c. Let B's rate be b. A + B = 1/18, B + C = 1/30, and A = 2C. Substituting: 2C + B = 1/18 and B + C = 1/30. Subtracting: C = 1/18 - 1/30 = (5-3)/90 = 2/90 = 1/45. So C alone takes 45 days, A takes 45/2 = 22.5 days. B = 1/30 - 1/45 = (3-2)/90 = 1/90, so B alone takes 90 days.

Multiple choice

A and B complete a work in 80 days and 96 days, respectively. They completed the work in 32 days with the help of C, How many days will C take to complete the entire work alone?

  1. 84

  2. 108

  3. 120

  4. 92
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A's 1 day work = 1/80, B's = 1/96. Together with C, they finish in 32 days, so combined rate = 1/32. C's rate = 1/32 - (1/80 + 1/96) = 1/32 - (12/960 + 10/960) = 1/32 - 22/960 = 30/960 - 22/960 = 8/960 = 1/120. So C alone takes 120 days.