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

The efficiencies of A, B and C are in the ratio of (2.5:3.5:5.5). Working together, they can complete a task in 13 days. In how many days will A alone complete 39% of the task?
  1. $23.389 days$
  2. $23.365 days$
  3. $23.356 days$
  4. $23.322 days$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Efficiencies 2.5:3.5:5.5 means work rates are proportional to these values. Combined rate = 11.5k, completing work in 13 days. A's rate = 2.5k. A alone would take 13 × 11.5/2.5 = 59.8 days for full work. For 39% of work: 59.8 × 0.39 ≈ 23.322 days.

Multiple choice

15 men take 21 days working 8 hour each day to do a piece of work. How many days of 6 hour each would 21 women take, if 3 women can do as much work as 2 men can do. 15 आदमी 8 घंटे प्रतिदिन कार्य करके किसी कार्य को 21 दिनों में पूरा करते हैं | 21 महिलायें 6 घंटे प्रतिदिन कार्य करके कितने दिन लेंगीं, यदि 3 महिलायें 2 आदमियों के बराबर कार्य करती हैं ?

  1. 20

  2. 24

  3. 27

  4. 25

  5. 30
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Total work = 15×21×8 = 2520 man-hours. 3 women = 2 men, so 1 woman = 2/3 man. 21 women = 21×(2/3) = 14 men. Let days = d. 14×d×6 = 2520. 84d = 2520. d = 30 days.

Multiple choice

40 men can complete a work in 15 days. If the same work is to be completed 3 days before how many more men should be employeed? 40 व्यक्ति एक कार्य को 15 दिनों में पूरा कर सकते है। यदि वही कार्य 3 दिन पहले पूरा करना हो तो कितने अतिरिक्त व्यक्तियों की आवश्यकता पडे़गी?

  1. 8

  2. 3

  3. 15

  4. 10

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

Total work = 40 × 15 = 600 man-days. New time = 12 days. Men needed = 600/12 = 50. Additional men = 50 - 40 = 10.

Multiple choice

In each of the following questions, read the given statement and compare the Quantity I and Quantity II on its basis. 24 men can do a work in 20 days and 36 women can do the same work in 24 days Quantity I : Time taken by 15 men to complete whole work Quantity II : Time taken by 16 women to complete whole work.

  1. Quantity : I > Quantity : II

  2. Quantity : I ≥ Quantity : II

  3. Quantity : I < Quantity : II

  4. Quantity : II ≥ Quantity : I

  5. Quantity I = Quantity II or relation can't be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

24 men complete work in 20 days, so 1 man's 1 day work = 1/(24*20). 15 men's 1 day work = 15/(24*20) = 1/32, so time = 32 days. 36 women complete in 24 days, so 1 woman's 1 day work = 1/(36*24). 16 women's 1 day work = 16/(36*24) = 1/54, so time = 54 days. Quantity I (32 days) < Quantity II (54 days).

Multiple choice

A can complete a work in 10 days, B in 12 days and C in 15 days. All of them began the work together, but A had to leave the work after 2 days of the start and B 3 days before the completion of the work. How long did the work last?

  1. 7 days

  2. 5 days

  3. 3 days

  4. 6 days

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

Total work = LCM(10,12,15) = 60 units. Rates: A = 6, B = 5, C = 4 units/day. All work together for 2 days: 15 × 2 = 30 units done, 30 left. B leaves 3 days before completion, so B works 4 days total (2 + 4 = 6 total work duration): B does 5 × 4 = 20 units. Remaining 40 units done by A and C at 10 units/day = 4 days. Total = 2 + 4 = 6 days... Wait, let me recalculate: Days 1-2: all three work (30 done). Days 3-4: B and C work (20 done, 50 total). Days 5-7: only C works (12 done, 62 total - exceeds 60). This doesn't work. Correct approach: Let total days = d. A works 2 days, B works (d-3) days, C works d days. 6×2 + 5×(d-3) + 4×d = 60. 12 + 5d - 15 + 4d = 60. 9d - 3 = 60. 9d = 63. d = 7.

Multiple choice

The total number of men, women and children working in a factory is 18. They earn Rs 4000 in a day. If the sum of the wages of all men, all women and all children is in the ratio of 18: 10: 12 and if the wages of an individual man, woman and child is in the ratio 6: 5 : 3, then how much a woman earn in a day?

  1. Rs 150

  2. Rs 100

  3. Rs 180

  4. Rs 220

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

Let total wages for men, women, children be 18x, 10x, 12x. Total = 40x = 4000, so x = 100. Women's total = 1000. Individual wages are 6k, 5k, 3k. Total people = 18x/(6k) + 10x/(5k) + 12x/(3k) = 900/k = 18, so k = 50. One woman earns 5k = Rs 250. Since 250 is not in options, answer is None of these (option E).

Multiple choice

If 12 men or 20 women can do a piece of work in 54 days, then in how many days can 9 men and 12 women together do the work? यदि 12 पुरुष या 20 महिलाएं किसी काम को 54 दिनों में कर सकते हैं, तो 9 पुरुष और 12 महिलाएं मिलकर उस काम को कितने दिन में कर सकते हैं?

  1. 35 days 35 दिन

  2. 40 days 40 दिन

  3. 25 days 25 दिन

  4. 20 days 20 दिन

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

12 men = 20 women can do work in 54 days. 1 man = 20/12 = 5/3 women. 9 men + 12 women = 9×(5/3) + 12 = 15 + 12 = 27 women. 20 women take 54 days, so 27 women take 54×20/27 = 54×20/27 = 40 days.

Multiple choice

In each of the following questions, read the given statement and compare the Quantity I and Quantity II on its basis. Anay can do the half of the work in 18 days and Meera can do the whole work in 30 days. Quantity I: In how many days will Anay and Meera do the whole work? Quantity II: If Anay starts the work and works for 3 days, after that Meera join him, in how many days will the whole work be completed?

  1. Quantity : I > Quantity : II

  2. Quantity : I ≥ Quantity : II

  3. Quantity : I < Quantity : II

  4. Quantity : II ≥ Quantity : I

  5. Quantity I = Quantity II or relation can't be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Anay completes half work in 18 days, so full work in 36 days (rate = 1/36). Meera's rate = 1/30. Combined rate = 1/36 + 1/30 = 11/180, so together they complete work in 180/11 ≈ 16.36 days. Quantity II: Anay works 3 days (3/36 = 1/12 work done), remaining 11/12 by both at 11/180 rate = 15 days. Total = 3 + 15 = 18 days. Since 16.36 < 18, Quantity I < Quantity II.

Multiple choice

The efficiencies of A, B and C are in the ratio 2 : 5 : 7 working together, they can complete a work in 10 days. In how many days will, A alone be able to complete 30% of that work?

  1. 20

  2. 28

  3. 30

  4. 21

  5. 25
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Efficiency ratio 2:5:7 means total efficiency units = 2+5+7 = 14. Working together, they complete the work in 10 days, so total work = 14 × 10 = 140 units. A's efficiency is 2 units/day, so A alone would take 140/2 = 70 days to complete the full work. For 30% of work (0.3 × 140 = 42 units), A would take 42/2 = 21 days. Option D is correct.

Multiple choice

14 men can complete a piece of work in 15 days and 15 women can complete the same piece of work in 20 days. What is the respective ratio between the amount of work done by 20 men in 1 day and the amount of work done by 18 women in 1 day? 14 पुरुष एक कार्य को 15 दिनों में पूरा कर सकते हैं और 15 महिलाएं उसी कार्य को 20 दिनों में पूरा कर सकती हैं। 1 दिन में 20 पुरुषों द्वारा किए गए कार्य की मात्रा और 1 दिन में 18 महिलाओं द्वारा किए गए कार्य की मात्रा के बीच संबंधित अनुपात कितना है?

  1. 100: 63

  2. 63: 100

  3. 4 :7

  4. 13 :15

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

14 men complete the work in 15 days, so 1 man's 1-day work = 1/210. 15 women complete in 20 days, so 1 woman's 1-day work = 1/300. Work by 20 men in 1 day = 20/210 = 2/21. Work by 18 women in 1 day = 18/300 = 3/50. The ratio is (2/21) : (3/50) = 100 : 63.

Multiple choice

A and B together can do a piece of work in 12 days, which B and C together can do in 16 days. After A has been working at it for 5 days and B for 7 days, C finishes it in 13 days. In how many days C alone will do the work? A और B एक साथ एक कार्य को 12 दिनों में कर सकते हैं, जिसे B और C मिलकर 16 दिनों में कर सकते हैं। A द्वारा उस पर 5 दिनों तक और B द्वारा 7 दिनों तक काम करने के बाद, C उसे 13 दिनों में पूरा करता है। C अकेले उस कार्य को कितने दिनों में करेगा?

  1. 22 days 22 दिन

  2. 24 days 24 दिन

  3. 20 days 20 दिन

  4. 25 days 25 दिन

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

A + B = 1/12 work/day, B + C = 1/16 work/day. Work done: A worked 5 days, B worked 7 days, C worked 13 days. So 5A + 7B + 13C = 1 (complete work). Substituting A = 1/12 - B and C = 1/16 - B: 5(1/12 - B) + 7B + 13(1/16 - B) = 1. Solving: 5/12 + 13/16 + (7 - 5 - 13)B = 1. This gives -11B = 1 - 5/12 - 13/16 = -11/48, so B = 1/48. Then C = 1/16 - 1/48 = 1/24. So C alone takes 24 days.

Multiple choice

2 men can complete a work in 15 days working 8 hours a day. The same work is completed by 3women working 4 hours a day for 16days. Find the time taken by a boy whose efficiency is 50% more than a woman and working 2 hours a day?

  1. 64days

  2. 32days

  3. 28days

  4. 54days

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

First find the work: 2 men × 15 days × 8 hours = 240 man-hours. Same work done by 3 women × 16 days × 4 hours = 192 woman-hours. So 240 man-hours = 192 woman-hours, meaning 1 man = 0.8 woman or 1 woman = 1.25 men. Boy's efficiency is 50% more than woman, so 1 boy = 1.5 women = 1.5 × 1.25 = 1.875 men. Time = 240 / (1.875 × 2) = 64 days.

Multiple choice

A contractor employed 30 men to complete the project in 100 days. But later on he realised that just after 25 days only 20% of the work had been completed. To complete the work on the scheduled time how many men he has to increase? एक ठेकेदार ने परियोजना को 100 दिनों में पूरा करने के लिए 30 पुरुषों को नियुक्त किया। लेकिन बाद में उन्होंने महसूस किया कि 25 दिनों के बाद केवल 20% काम ही पूरा हुआ था। निर्धारित समय पर कार्य को पूरा करने के लिए उसे कितने पुरुषों की वृद्धि करनी होगी?

  1. 10

  2. 40

  3. 30

  4. 20

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

30 men × 100 days = 3000 man-days required. In 25 days with 30 men: 30 × 25 = 750 man-days of work capacity, but only 20% (600 man-days) of work was completed. This means efficiency = 600/750 = 0.8 or 80%. Remaining work = 80% × 3000 = 2400 man-days. Remaining days = 100 - 25 = 75 days. At 80% efficiency, effective capacity = 75 × 0.8 = 60 man-days/day equivalent. Men needed = 2400/60 = 40 men. Increase = 40 - 30 = 10 men.

Multiple choice

A alone complete the work in x days and B alone complete the work in (x + 32) days. If A and B started the work together, after 6 days they complete the 20% of the work, in how many days A alone complete the work? A अकेले कार्य को x दिनों में पूरा करता है और B अकेले कार्य को (x + 32) दिनों में पूरा करता है। यदि A और B एक साथ काम शुरू करते हैं, तो 6 दिनों के बाद वे काम का 20% पूरा करते हैं, A अकेले उस काम को कितने दिनों में पूरा करेगा?

  1. 44 days 44 दिन

  2. 45 days 45 दिन

  3. 42 days 42 दिन

  4. 48 days 48 दिन

  5. 50 days 50 दिन
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let total work = 1 unit. A's rate = 1/x and B's rate = 1/(x+32). Together their rate = 1/x + 1/(x+32). In 6 days they complete 20% (0.2) of work: 6(1/x + 1/(x+32)) = 0.2. Solving: 6(x+32 + x)/x(x+32) = 0.2, so 12x + 192 = 0.2x² + 6.4x. Rearranging: 0.2x² - 5.6x - 192 = 0, or x² - 28x - 960 = 0. Using quadratic formula: x = [28 ± √(784 + 3840)]/2 = [28 ± √4624]/2 = [28 ± 68]/2. So x = 48 (positive root). A alone takes 48 days.