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

12 men and 16 boys can do a piece of work in 5 days and 13 men and 24 boys can do it in 4 days. Compare the daily work done by a man with that done by a boy. 2 पुरुष और 16 लड़के किसी काम को 5 दिनों में कर सकते हैं और 13 पुरुष और 24 लड़के 4 दिनों में कर सकते हैं। एक आदमी द्वारा किए गए दैनिक कार्य की तुलना एक लड़के द्वारा किए गए दैनिक कार्य से करें।

  1. 2:1

  2. 4:5

  3. 8:9

  4. 4:3

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

Let 1 man's daily work = m, 1 boy's daily work = b. From given: 60m + 80b = 1/5 and 52m + 96b = 1/4. Solving gives b = 1/600, m = 1/300. Therefore m:b = (1/300):(1/600) = 2:1. Option A is correct. (Note: The Hindi text incorrectly says '2 men' instead of '12 men')

Multiple choice

To do certain work, the ratio of efficiency of A and that of B is 3:7. Working together, they can complete in 10.5 days. they work together for 8 days. 60 % of remaining work will be completed by A alone in किसी कार्य को करने के लिए A और B की कार्यकुशलता का अनुपात 3:7 है। एक साथ काम करते हुए, वे 10.5 दिनों में पूरा कर सकते हैं। वे 8 दिनों तक एक साथ काम करते हैं। शेष कार्य का 60% अकेले A द्वारा में पूरा किया जाएगा

  1. 10 days 10 दिन

  2. 5 days 5 दिन

  3. 12 days 12 दिन

  4. 7 days 7 दिन

  5. 11 days 11 दिन
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Efficiency ratio A:B = 3:7. Combined rate = 10 units/day, work = 10 × 10.5 = 105 units. In 8 days, they complete 80 units, leaving 25 units. A's rate = 3 units/day. 60% of 25 = 15 units. Time for A = 15/3 = 5 days. Option B is correct.

Multiple choice

Working 7 hours in a day, 4 men can do a piece of work in 8 days. Working 8 hours in a day, the required number of men to perform the same work in 4 days will be एक दिन में 7 घंटे काम करते हुए, 4 आदमी एक काम को 8 दिनों में पूरा कर सकते हैं। एक दिन में 8 घंटे कार्य करते हुए समान कार्य को 4 दिनों में करने के लिए पुरुषों की आवश्यक संख्या होगी

  1. 8

  2. 4

  3. 7

  4. 9

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

Work = men × hours × days = 4 × 7 × 8 = 224 man-hours. For the second scenario: 224 = M × 8 × 4 = 32M, so M = 224/32 = 7 men. The work remains constant, so the product of men, hours, and days must equal 224.

Multiple choice

A can do one - third of a work in 15 days, B can do 75% of the same work in 18 days and C can do the same work in 36 days. B and C work together for 8 days. In how many days will A alone complete the remaining work? A एक काम का एक तिहाई 15 दिनों में कर सकता है, B उसी काम का 75% 18 दिनों में और C उसी काम को 36 दिनों में कर सकता है। B और C एकसाथ 8 दिनों तक कार्य करते हैं। A अकेला शेष कार्य को कितने दिनों में पूरा करेगा?

  1. 25 days 25 दिन

  2. 20 days 20 दिन

  3. 12 days 12 दिन

  4. 6 days 6 दिन

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

A does 1/3 work in 15 days, so complete work in 45 days (rate = 1/45). B does 75% in 18 days, so complete work in 24 days (rate = 1/24). C does complete work in 36 days (rate = 1/36). B and C together for 8 days complete 8×(1/24 + 1/36) = 8×(3/72 + 2/72) = 8×5/72 = 40/72 = 5/9 of work. Remaining work = 4/9. A alone does 4/9 work at rate 1/45, so time = (4/9)/(1/45) = (4/9)×45 = 20 days.

Multiple choice

A can finish a piece of work in 48 days and B can finish it in 60 days. They work together for 12 days and then A goes away. In how much time (in days and hours) will B finish 25% of the remaining work?

  1. 6 days 4 hours

  2. 8 days 8 hours

  3. 6 days 6 hours

  4. 8 days 6 hours
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A's work rate = 1/48 per day, B's = 1/60 per day. Combined rate = 1/48 + 1/60 = 9/240 = 3/80 per day. In 12 days, they complete 12 × 3/80 = 36/80 = 9/20 of work. Remaining work = 11/20. B must finish 25% of this = (1/4) × (11/20) = 11/80. At B's rate of 1/60 per day, time = (11/80) / (1/60) = (11/80) × 60 = 660/80 = 33/4 = 8.25 days = 8 days 6 hours.

Multiple choice

A can complete 25% of a work in 15 days. He works for 15 days and then B alone finishes the remaining work in 30 days. In how many days will A and B working together finish 50% of the same work?

  1. 25

  2. 24

  3. 20

  4. 12
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A completes 25% work in 15 days, so total work for A = 60 days. A's rate = 1/60 per day. A works for 15 days, completing 15/60 = 1/4 of work. Remaining work = 3/4. B completes 3/4 work in 30 days, so B's rate = (3/4)/30 = 1/40 per day. Combined rate of A + B = 1/60 + 1/40 = 5/240 = 1/24 per day. For 50% (1/2) of work: time = (1/2)/(1/24) = 12 days, matching option D.

Multiple choice

A certain number of men can do a work in 60 days. If there were 15 men more it could be finished in 10 days less. How many men were there in the beginning ?

  1. 60

  2. 70

  3. 75

  4. 80
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let M = initial men, work = M × 60 man-days. With M + 15 men: (M + 15) × 50 = M × 60. Solve: 50M + 750 = 60M → 750 = 10M → M = 75. Verification: 75 men can do work in 60 days. 90 men (75 + 15) would take 75 × 60 / 90 = 50 days, which is 10 days less.

Multiple choice

Two men A and B can complete a piece of work in 10 days and 15 days respectively.They started the work together but A left after 3 days and another person C joins the who can complete the work in 30 days. In how many days the work got completed ?

  1. 6 days

  2. 7days

  3. 10 days

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

A and B together complete 1/10 + 1/15 = 1/6 of the work daily. In 3 days, they finish 3/6 = 1/2 of the work. The remaining 1/2 is completed by B and C working together at 1/15 + 1/30 = 1/10 per day, taking 5 more days. Total time = 3 + 5 = 8 days.

Multiple choice

Shivam alone can complete a piece of work in 10 days and Satyam alone can complete the same work in 40 days. If they work on alternate days with Shivam starting the work, then in how many days will the work be completed?

  1. 12

  2. 15

  3. 20

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

Shivam's 1-day work = 1/10, Satyam's = 1/40. In 2 days, they complete 1/10 + 1/40 = 5/40 = 1/8. After 14 days (7 pairs), 7 × 1/8 = 7/8 done. Day 15: Shivam does 1/10, total 7/8 + 1/10 = 35/40 + 4/40 = 39/40. Day 16: Satyam does 1/40, total = 40/40 = 1 (complete).

Multiple choice

P can complete a work in 12 days working 8 hours a day. Q can complete the same work in 8 days working 10 hours a day. If both P and Q work together, working 8 hours a day then in how many days can they complete the work?

  1. 60/11 days

  2. 60 days

  3. 60/9 days

  4. 55 days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

P की कुल कार्य क्षमता 12 x 8 = 96 घंटे है, इसलिए P का एक घंटे में 1/96 कार्य होगा। Q की कुल क्षमता 8 x 10 = 80 घंटे है, इसलिए Q का एक घंटे में 1/80 कार्य होगा। दोनों मिलकर एक घंटे में (1/96 + 1/80) = 11/480 कार्य करेंगे। पूरा कार्य 480/11 घंटे में होगा, जो 8 घंटे प्रतिदिन पर 60/11 दिन है।

Multiple choice

A is as efficient as B and C together. Working together A and B can complete a work in 18 days and C alone in 30 days. If A and C worked for 8 days then the remaining work is completed by B in how many days? A, उतना ही कार्यकुशल है जितना B और C के साथ मिलकर। A और B एक साथ मिलकर एक काम को 18 दिनों में और C अकेले 30 दिनों में पूरा कर सकते हैं। यदि A और C ने 8 दिनों तक कार्य किया तो शेष कार्य B द्वारा कितने दिनों में पूरा किया जाएगा?

  1. 34 days 34 दिन

  2. 28 days 28 दिन

  3. 30 days 30 दिन

  4. 36 days 36 दिन

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

A = B + C in efficiency. A + B = 1/18, C = 1/30. Substituting: B + C + B = 1/18, so 2B + 1/30 = 1/18. Solving: 2B = 1/18 - 1/30 = 1/45, thus B = 1/90. A = 1/90 + 1/30 = 2/45. A + C work 8 days: 8*(2/45 + 1/30) = 28/45. Remaining 17/45 done by B: (17/45)/(1/90) = 34 days.

Multiple choice

If 4 men and 6 boys can do a work in 8 days and 6 men and 4 boys can do the same work in 7 days, then how many days will 5 men and 4 boys take to do the same work?

  1. 5

  2. 8

  3. 6

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

Let one man's work per day be m and one boy's work per day be b. From given: 4m + 6b = 1/8 and 6m + 4b = 1/7. Solving these equations gives m = 1/56 and b = 1/112. For 5 men and 4 boys: daily work = 5/56 + 4/112 = 5/56 + 2/56 = 7/56 = 1/8. Therefore, they complete the work in 8 days.