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 3 men or 6 women can do a piece of work in 16 days, in how many days can 8 men and 8 women do the same piece of work? यदि 3 आदमी या 6 औरतें एक काम को 16 दिनों में कर सकते हैं, 8 आदमी और 8 औरतें उसी कार्य को कितने दिनों में कर सकते हैं ?

  1. 4 days/दिन

  2. 5 days/दिन

  3. 3 days/दिन

  4. 2 days/दिन
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

From the given information, 3 men's work = 6 women's work, so 1 man = 2 women. The total work is 3 × 16 = 48 man-days. Converting 8 men and 8 women to men: 8 men + 4 men = 12 men total. Days needed = 48/12 = 4 days. The key is converting women to equivalent men using the rate relationship.

Multiple choice

Prakash is thrice as good as Neeraj. They together can do a job in 16 days, in how many days will Neeraj finish the work alone?

  1. 46 days

  2. 52 days

  3. 64 days

  4. 68 days

  5. 72 days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If Prakash is thrice as efficient as Neeraj, let Neeraj's efficiency = 1 unit/day, then Prakash's = 3 units/day. Combined efficiency = 4 units/day. Total work = 4 × 16 = 64 units. Neeraj alone = 64/1 = 64 days. The distractors 52, 68, and 72 days come from incorrect ratio setups or calculation errors.

Multiple choice

20 men can finish a work in 30 days. After 10 days, 10 men leave the work, remaining men work for the next 10 days. How many more men will be required after 20 days from the start of the work to complete the work in time?

  1. 25

  2. 20

  3. 15

  4. 10

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

Total work = 20×30 = 600 man-days. First 10 days: 20 men complete 200 units. Next 10 days: 10 men complete 100 units. Remaining 20 days: work = 600-300 = 300 units, requiring 300/20 = 15 men. Since only 10 men remain, need 15-10 = 5 more men - but this gives 15 men for 20 days = 300 units. Actually, check: 10 men for 20 days = 200 units, but need 300. So need 300/20 = 15 men total, meaning 15-10 = 5 more men needed. Wait, options suggest 20 more men - rechecking: After 20 days, 300 work done, 300 remains. With 20 days left, need 300/20 = 15 men. Have 10, need 5 more. But answer claims 20 more men (total 25) - let's verify: 25×20 = 500, but only 300 needed. There's a calculation mismatch.

Multiple choice

P can do (\frac{1}{4}) part of a work in 10 days, Q can do 40% of that work in 15 days, R can do (\frac{1}{3}) part of that work in 13 days and S can do (\frac{1}{6}) part of that work in 7 days. Who can do that work in minimum time ?

  1. P

  2. Q

  3. R

  4. S

  5. Cannot be determined
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Calculate each person's rate: P does 1/4 work in 10 days, so full work in 40 days. Q does 40% (2/5) work in 15 days, so full work in 15 × 5/2 = 37.5 days. R does 1/3 work in 13 days, so full work in 39 days. S does 1/6 work in 7 days, so full work in 42 days. Q completes work fastest (37.5 days), so Q is the answer.

Multiple choice

A man and a woman working together can do a certain work in 20 days. Their skill in doing the work in the ratio 3 : 2. How many days will the woman take to finish the work alone? एक पुरूष और एक स्त्री साथ-साथ काम करते हुए एक कार्य 20 दिनों में पूरा कर सकते हैं। उस कार्य को करने में उनकी दक्षता का अनुपात 3 : 2 रहता है। तद्नुसार उस स्त्री को अकेले वह कार्य पूरा करने में कितने दिन लगेगे?

  1. 50 days / दिन

  2. 45 days / दिन

  3. 60 days / दिन

  4. 54 days / दिन
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the man's efficiency be 3x and woman's efficiency be 2x. Combined efficiency = 5x work/day. They complete work in 20 days, so total work = 20 × 5x = 100x units. Woman alone at 2x efficiency would take 100x/2x = 50 days. Option B (45 days) would require different efficiency ratios. Option C (60 days) assumes equal efficiency. Option D (54 days) is a miscalculation.

Multiple choice

A takes 10 days less than the time taken by B to finish a piece of work. If both A & B can do it in 12 days, then the time taken by B alone to finish the work is- एक कार्य पूरा करने में A को B की तुलना में 10 दिन कम लगते हैं। यदि A तथा B दोनों मिलकर वह कार्य 12 दिनों में पूरा कर सकते हों तो अकेले B को वह कार्य पूरा करने में कितना समय लगेगा?

  1. 30 days / दिन

  2. 27 days / दिन

  3. 20 days / दिन

  4. 25 days / दिन
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let B take x days alone. Then A takes (x-10) days alone. Their combined rate: 1/(x-10) + 1/x = 1/12. Solving: (x + x - 10)/[x(x-10)] = 1/12, so (2x-10)×12 = x(x-10). This gives 24x - 120 = x² - 10x, or x² - 34x + 120 = 0. Solving: x = [34 ± √(1156 - 480)]/2 = [34 ± √676]/2 = [34 ± 26]/2. So x = 30 or x = 4. Since A takes (x-10) days, x cannot be 4. Thus x = 30 days.

Multiple choice

A man and a women, working together, can complete a piece of work in 33 days. The ratio of their efficiencies of working of a male and a female is 14 : 11. In how many days will a woman working alone complete the work? एक पुरूष और महिला एक साथ एक काम को 33 दिनों में समाप्त कर सकते है । एक पुरुष और एक महिला के काम करने की क्षमता का अनुपात 14 : 11 है। एक महिला अकेले इस काम को कितने दिनों में समाप्त करेगी?

  1. 65 days/दिन

  2. 75 days/दिन

  3. 85 days/दिन

  4. 102 days/दिन
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let man's efficiency = 14k, woman's = 11k. Together: 25k work/day. In 33 days, work = 33 × 25k = 825k. Woman alone: 825k/(11k) = 75 days. Check: Together rate = 1/33, woman rate = 11/25 of together = 11/(25×33) = 11/825 = 1/75.

Multiple choice

30 children can do a piece of work in 16 days. How many children would be required to do the same work in 20 days?

  1. 12

  2. 24

  3. 36

  4. 48

  5. 60
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

This is an inverse proportion problem - more children means fewer days. Total work = 30 × 16 = 480 child-days. To complete in 20 days, children needed = 480/20 = 24. Option A (12) would give 12×20 = 240 child-days, half the required work. Option C (36) would give 36×20 = 720 child-days, exceeding the requirement.

Multiple choice

Ram and Shyam work on a job together for four days and complete 60% of it. Ram takes leaves then for eight days to complete the job. How long would Ram take to complete the entire job alone and Shyam works? राम और श्याम एक साथ एक कार्य को चार दिन के लिए करते हैं और 60% काम पूरा करता है। राम छुट्टी लेता है, और तब श्याम काम को पूरा करने के लिए 8 दिन अधिक लेता है तो राम को अकेले काम करने में कितना समय लगेगा ?

  1. 6 days/ दिन

  2. 8 days/ दिन

  3. 10 days/ दिन

  4. 11 days/ दिन
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Ram and Shyam together complete 60% in 4 days, so 100% would take them 4 × (100/60) = 20/3 days together. Let Ram take R days alone, Shyam take S days alone. Their combined rate: 1/R + 1/S = 3/20. Shyam completes remaining 40% alone in 8 days, so 100% takes S = 8 × (100/40) = 20 days. Therefore: 1/R = 3/20 - 1/20 = 2/20 = 1/10, so R = 10 days.

Multiple choice

The following questions are accompanied by three statements I, II, and III. You have to determine which statement(s) is/are necessary/sufficient to answer the question? In how many days can the work be done by 9 men and 15 women? I. 6 men and 5 women can complete the work in 6 days. II. 3 men and 4 women can complete the work in 10 days. III. 18 men and 15 women can complete the work in 2 days.

  1. Only I

  2. Only II

  3. Any two

  4. All I, II and III

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

Let m = 1 man's work/day, w = 1 woman's work/day. From I: 6(6m+5w)=1, so 36m+30w=1. From II: 10(3m+4w)=1, so 30m+40w=1. Solving gives m=1/54, w=1/90. For 9 men and 15 women: daily work = 9/54 + 15/90 = 1/6 + 1/6 = 1/3. Time needed = 3 days. Similarly, II and III together also work (I and III give same equation). Any two statements are sufficient.

Multiple choice

A and B can do work in 12 days .B and C in 15 days and C and A in 20 days.They all work together for 6 days and then A left.In how many more days can B and C finish the remaining work? A और B काम को 12 दिनों में कर सकते है, B और C, 15 दिनों में तथा और C और A 20 दिनों में वे सभी एक साथ 6 दिन के लिए काम करते है, और तब A काम छोड़ देता है। B और C शेष काम को कितने और दिनों में पूरा करेगे?

  1. 4 days

  2. 5 days

  3. 6 days

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

A+B rate = 1/12, B+C = 1/15, C+A = 1/20. Adding: 2(A+B+C) = 1/12+1/15+1/20 = 1/5, so A+B+C = 1/10 (all three take 10 days together). In 6 days, they complete 6/10 = 3/5 work. Remaining 2/5 work at B+C rate (1/15) takes (2/5)/(1/15) = 6 days.

Multiple choice

A can do a piece of work in 24 days, B in 32 days and C in 64 days. All begin to do it together but A leaves after 6 days and B leaves 6 days before the completion of the work. The total number of days they worked for is - A एक काम को 24 दिनों में कर सकता है। B, 32 दिनों में और C, 64 दिनों में कर सकते है। सभी ने एक साथ काम शुरू किया परन्तु A, 6 दिन बाद छोड़ देता है और B काम पूरा होने के 6 दिन पहले छोड़ देता है, तो वे कुल कितने दिन काम करते हैं?

  1. 20 days/दिन

  2. 8 days/दिन

  3. 16 days/दिन

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

A's rate = 1/24, B's = 1/32, C's = 1/64. Total work = 1. Let total days = D. A works 6 days, B works (D-6) days (leaves 6 days before completion), C works D days. Equation: 6(1/24) + (D-6)(1/32) + D(1/64) = 1. Solving: D = 20 days. Option A is correct.

Multiple choice

A village road is to be construction by a team of 250 workers. After 12 days it was found that only 2/7 th part of the work was completed. To complete the rest in another 25 days, how many more workers should be employed? एक गांव की सड़क 250 मजदूर की एक टीम के द्वारा बनायी गयी। 12 दिनों के बाद यह पाया गया कि केवल काम का 2/7 भाग पूरा हुआ। शेष भाग को अन्य 25 दिनों में पूरा करने के लिये कितने और मजदूरों को काम पर लगाया जाना चाहिए?

  1. 53

  2. 52

  3. 50

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

Work done in 12 days by 250 workers = 2/7. Work remaining = 5/7 to be done in 25 days. Required workers: (250 × 12)/(2/7) = (W × 25)/(5/7). Solving: W = 300. Additional workers = 300 - 250 = 50. Option C is correct.