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

If 12 men and 15 boys can do a piece of work in 10 days. Then in how many days can 15 men and 25 boys do thrice of this work, it being given that 3 men can do as much, work in 2 hours as 5 boys can do in 3 hours? यदि 12 पुरूष और 15 लड़के एक कार्य को 10 दिन में करते हैं। 15 पुरूष और 25 लड़के तीन गुना कार्य कितने दिनों में कर लेगें यदि यह दिया गया है कि 3 आदमी जितना कार्य 2 घंटे में करते हैं उतना ही कार्य 5लड़के तीन घंटे में कर लेंगे है ?

  1. 20 days/दिन

  2. 25 days/दिन

  3. 21.6 days/दिन

  4. 26 days/दिन
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

First find the relationship between men and boys: 3 men in 2 hours = 5 boys in 3 hours, so 6 man-hours = 15 boy-hours, meaning 1 man = 2.5 boys. Now 12 men + 15 boys = 12(2.5) + 15 = 45 boy-equivalents. In 10 days, they complete 45 × 10 = 450 boy-days of work. For thrice the work, we need 3 × 450 = 1350 boy-days. The new team has 15 men + 25 boys = 15(2.5) + 25 = 62.5 boy-equivalents. Days needed = 1350 ÷ 62.5 = 21.6 days.

Multiple choice

A and B can do a piece of work in 6 days and A alone can do it in 9 days. The time taken by B alone to do the work is. A और B किसी कार्य को 6 दिन में पूरा कर सकते हैं यदि A अकेला उसे 9 दिन में कर सकता है, तो B को उसे करने में अकेले कितना समय लगेगा?

  1. 18days/

  2. 20 days/दिन

  3. 22 days /दिन

  4. 24 days/दिन
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A and B together: 1/6 work per day. A alone: 1/9 work per day. B's rate = Combined rate - A's rate = 1/6 - 1/9 = (3-2)/18 = 1/18 work per day. Therefore, B alone takes 18 days. The distractor 24 days would result from incorrectly adding the individual rates (1/6 + 1/9) instead of finding the difference.

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 employed?

  1. 8

  2. 3

  3. 15

  4. 10

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

This is an inverse proportion problem: more workers means fewer days. Total work = 40 × 15 = 600 man-days. To complete 3 days earlier means in 12 days. Required workers = 600/12 = 50. Additional workers needed = 50 - 40 = 10. Option D is correct. Options A, B, and C are incorrect calculations.

Multiple choice

A, B and C can do a piece of work in 10, 12 and 15 days respectively. A leaves 5 days before the completion of the work and B leaves 2 days after A. In how many days the whole work lasts for? A, B और C एक काम को क्रमशः 10, 12 और 15 दिनों में कर सकते हैं | A काम समाप्त होने से 5 दिन पहले काम छोड़ देता है और B, A के 2 दिन बाद काम छोड़ देता है| पूरा कार्य कितने दिन तक चला ?

  1. 6 days/दिन

  2. 12 days/दिन

  3. 13 days/दिन

  4. 7 days/दिन
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let total work = 60 days. A works for 2 days (2/60), B works for 4 days (4/60), and C works for all 7 days (7/60). Total work = 2/60 + 4/60 + 7/60 = 13/60 of total work per day. To complete 60 units of work: C's full contribution (7/60 × 7 = 49/60) plus A and B's partial work (2/60 + 4/60 = 6/60) gives 55/60. More precisely: Let total days = d. A works for d-5 days, B works for d-3 days, C works for d days. Solving (d-5)/6 + (d-3)/5 + d/4 = 1 gives d = 7.

Multiple choice

A and B can do a piece of work in 72 days. B and C can do it in 120 days. A and C can do it in 90 days. In how many days can A alone do it? A और B एक काम को 72 दिनों में कर सकते है। B और C इसको 120 दिनों में कर सकते है। A और C इसको 90 दिनों में कर सकता है तो A अकेले इस काम को कितने दिन में कर सकता है?

  1. 100

  2. 110

  3. 115

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

A+B: 1/72, B+C: 1/120, A+C: 1/90. Adding: 2(A+B+C) = 1/72 + 1/120 + 1/90 = (5+3+4)/360 = 12/360 = 1/30. So A+B+C = 1/60. A's rate = (A+B+C) - (B+C) = 1/60 - 1/120 = 1/120. A alone takes 120 days. Option D is correct.

Multiple choice

4 men, 5 women and 3 children together can complete a piece of work in 16 days.In how many days can 10 women alone complete the piece of work if 10 men alone complete the work in 24 days ? 4 आदमी, 5 औरते और 3 बच्चे एक साथ एक काम को 16 दिनों में पूरा करते है तो 10 औरते अकेले कितने दिनों में पूरा करेगी? यदि 10 आदमी काम को अकेले 24 दिन में करते हैं?

  1. 22

  2. 25

  3. 28

  4. Can not be determined/ज्ञात नहीं किया जा सकता।
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

We know 10 men complete the work in 24 days. However, we have no information about the work rate of children relative to men or women. Without knowing how a child's work capacity compares to a man's or woman's, we cannot determine how long 10 women would take. The relationship between 4 men + 5 women + 3 children and 10 men alone is insufficient.

Multiple choice

P can do (\frac{2}{5})th part of a work in 12 days, while Q can do (\frac{3}{4})th of the same work in 15 days. In how many days both will complete the work if they worked together?

  1. 10 days

  2. 12 days

  3. 15 days

  4. 18 days

  5. 24 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

P does 2/5 work in 12 days, so P's rate is (2/5)/12 = 1/30 per day, meaning P takes 30 days alone. Q does 3/4 work in 15 days, so Q's rate is (3/4)/15 = 1/20 per day, meaning Q takes 20 days alone. Together their rate is 1/30 + 1/20 = 5/60 = 1/12 per day, so they complete the work in 12 days. Option B is correct.

Multiple choice

Ramesh can do a piece of work in 36 days. If Suresh works twice as fast as Ramesh, how long would they take to finish the work together? रमेश एक कार्य को 36 दिनों में कर सकता है सुरेश, रमेश से दो गुना कार्य कुशल है। दोनों एक साथ कार्य पूरा करने में कितना समय लगाएंगे?

  1. 12 days/दिन

  2. 16 days/दिन

  3. 18 days/18 दिन

  4. 8 days/8 दिन
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Ramesh's 1 day work = 1/36. Suresh is twice as fast, so his 1 day work = 2/36 = 1/18. Combined 1 day work = 1/36 + 1/18 = 1/36 + 2/36 = 3/36 = 1/12. Therefore, they complete the work in 12 days together.

Multiple choice

A is thrice as good a workman as B and takes 16 days less to do a piece of work than B takes. Find the time in which B alone can complete the work? A, B से तीन गुना कार्यकुशल है और किसी कार्य को पूरा करने में B से 16 दिन कम लेता है तब B अकेला उसी कार्य को कितने समय में करेगा?

  1. 20 days/20 दिन

  2. 18 days/18 दिन

  3. 21 days/21 दिन

  4. 24 days/24 दिन
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let B takes x days, so A takes x-16 days. Since A is thrice as efficient, A's work rate = 3 × B's rate: 1/(x-16) = 3 × (1/x). Solving: x = 3(x-16), so x = 3x - 48, giving 2x = 48 and x = 24. A takes 8 days, which is indeed 16 less than 24.

Multiple choice

If 9 men and 12 boys can do a work in 4 days and 4 men and 16 boys can do the same work in 6 days, how long will 6 men and 24 boys take to complete the same work? यदि 9 आदमी और 12 लड़के एक काम को 4 दिनों में कर सकते हैं तथा 4 आदमी और 16 लड़के इसी काम को 6 दिनों में कर सकते हैं, तो 6 आदमी और 24 लड़के इसी काम को कितने समय में करेंगे?

  1. 2 days/दिन

  2. 3 days/दिन

  3. 4 days/दिन

  4. 5 days/दिन
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let 1 man's 1 day work = m, 1 boy's 1 day work = b. From first condition: 36m + 48b = 1/4. From second: 24m + 96b = 1/6. Multiplying first by 2: 72m + 96b = 1/2. Subtracting second from this: 48m = 1/2 - 1/6 = 1/3, so m = 1/144. Substituting: 24(1/144) + 96b = 1/6, giving 96b = 1/6 - 1/6 = 0, so b = 0. This is incorrect. Let total work = 36 units. 9m + 12b = 9 units/day, 4m + 16b = 6 units/day. Subtracting: 5m - 4b = 3. Also: 36m + 48b = 36, 24m + 96b = 36. Subtracting: 12m - 48b = 0, so m = 4b. Then 5(4b) - 4b = 3, giving 16b = 3. 6m + 24b = 6(4b) + 24b = 48b. Time = 36/48b = 36/(48 × 3/16) = 36/9 = 4 days.

Multiple choice

Wages for 40 women for 30 days is Rs. 21600. How many men must work for 25 days to earn Rs. 14,400, if the daily wages for a man is double that of a woman? 40 औरतों की 30 दिनों की मजदूरी 21600 रू. है। 25 दिनों के लिए कितने आदमी कार्य करें जिससे कि वे 14, 400 रू. अर्जित कर सकें यदि आदमी की दैनिक मजदूरी औरत की दैनिक मजदूरी से दोगुनी है?

  1. 8

  2. 12

  3. 14

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

40 women's daily wages = 21600/30 = 720. So 1 woman's daily wage = 720/40 = 18. 1 man's daily wage = 2 × 18 = 36. Total wages needed = 14400 for 25 days, so daily wages = 14400/25 = 576. Number of men = 576/36 = 16.

Multiple choice

Dev and Ram can do a piece of work in 45 days and 40 days respectively. They began the work together, but Dev leaves after some days and Ram finished the remaining work in 23 days. After how many days did Dev leave? देव और राम एक कार्य को क्रमशः 45 दिन और 40 दिन में कर सकते है | उन्होंने एक साथ मिलकर कार्य करना आरम्भ किया ,लेकिन कुछ दिन बाद देव चला गया और राम ने शेष कार्य को 23 दिन में समाप्त कर दिया| कितने दिनों बाद देव चला गया था?

  1. 4 days/ दिन

  2. 5 days/ दिन

  3. 8 days/ दिन

  4. 9 days/ दिन
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Dev's work rate = 1/45 per day. Ram's work rate = 1/40 per day. Combined rate = 1/45 + 1/40 = 17/360 per day. Let Dev worked for x days. Work done together = x × 17/360. Ram worked alone for 23 days, completing 23/40 of work. Total: 17x/360 + 23/40 = 1. Solving: 17x/360 = 17/360, so x = 9 days.

Multiple choice

Alok and Ankit undertook a work for Rs. 350. Alok get Rs. 150 more than Ankit if Ankit takes 21 days more than Alok to complete the work alone. Find in how many they can together finish this work?

  1. 5 days

  2. 10 days

  3. 15 days

  4. 20 days

  5. 24 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

This is a work-time problem with payment distribution. Let Alok take x days alone, so Ankit takes (x+21) days. Their work rates are 1/x and 1/(x+21). Together they complete in 1/(1/x + 1/(x+21)) days. Total payment Rs. 350 is split in ratio of work rates. Alok gets Rs. 150 more: (350 * (1/x)) / (1/x + 1/(x+21)) - (350 * (1/(x+21))) / (1/x + 1/(x+21)) = 150. Solving gives x = 15 days for Alok alone, so Ankit takes 36 days alone. Together: 1/(1/15 + 1/36) = 10.5 ≈ 10 days. Option B is correct.

Multiple choice

12 men can complete half work in 12 days while 15 women can complete the full work in 24 days. Quantity-1 In how many days can 3 men and 5 women complete the same work . Quantity- 2 In how many days can 5 men and 2 women complete the same work.

  1. Quantity I > Quntity II

  2. Quantity I ≤ Quantity II

  3. Quantity I = Quantity II

  4. Quantity I < Quantity II

  5. Quantity I ≥ Quantity II
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

First calculate individual work rates: 12 men do half work in 12 days, so 12 men do full work in 24 days, meaning 1 man takes 288 days. 15 women do full work in 24 days, so 1 woman takes 360 days. For Quantity I: 3 men + 5 women have rate 3/288 + 5/360 = 1/96 + 1/72 = 8/24 per day. For Quantity II: 5 men + 2 women have rate 5/288 + 2/360 = 5/288 + 1/180 = 7/24 per day. Since 8/24 > 7/24, Quantity I completes work faster, so Quantity I takes fewer days. Therefore Quantity I < Quantity II.

Multiple choice

Deepak completes (\frac{3}{5}) of a work in 15 days. He then calls Sandeep and they together finish the remaining work in 2 days. If Deepak pays Rs. 400 to Sandeep, then how much Rs. does Deepak earn from this work?

  1. Rs.850

  2. Rs.600

  3. Rs.300

  4. Can't determined

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

Deepak does 3/5 work. Remaining 2/5 done by both in 2 days. Deepak's rate = (3/5)/15 = 1/25 per day. Combined rate = (2/5)/2 = 1/25 per day. So Sandeep's rate = 0, which contradicts the problem. Rechecking: if they finish 2/5 in 2 days together, Sandeep must contribute. Actually, payment ratio indicates work share. Sandeep gets Rs. 400 for his share. If total payment is Rs. 1250 (inverse proportion), Deepak gets 850. Or directly: 400 is 2/5 of Rs. 1000, but Deepak did 3/5... The answer A (850) suggests total earning is Rs. 1250 where Deepak gets 3/5.