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 5 men and 3 women can complete a work in 15 days whereas 15 men and 9 women can complete this work in 5 days. Find in how many days 10 men and 6 women can complete this work?

  1. 10

  2. 7.5

  3. 8

  4. 9

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

Work equations: 75m + 45w = 75m + 45w gives 75m + 45w = 75m + 45w, which is consistent. This means 5m + 3w has same efficiency as 15m + 9w. Let m = -3w/5. Substituting in (10m + 6w)D = 75m + 45w gives D = 7.5 days.

Multiple choice

P and Q together can complete a work in 12 days. P alone can complete in 20 days.If Q does the work only half a day daily, then in how many days P and Q together will complete the work? P औए Q एक साथ मिलकर एक काम को 12 दिनों में कर सकते हैं | P अकेला इसे 20 दिनों में कर सकता है | यदि Q आधे दिन ही काम करे, तो P और Q मिलकर एकसाथ काम को कितने दिनों में कर लेंगें

  1. 10

  2. 20

  3. 11

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

P's one day work = 1/20. P+Q's one day work = 1/12. Therefore, Q's one day work = 1/12 - 1/20 = (5-3)/60 = 1/30. If Q works half-day daily, Q's contribution = 1/60 per day. Combined P+Q work = 1/20 + 1/60 = 4/60 = 1/15. Therefore, work completes in 15 days.

Multiple choice

A can do a piece of work in 36 days. B can complete the same work in 24 days whereas C can complete this work in 48 days. A started the work and after 12 days leave the work, then B work for next 6 days and left the job for C. In how many days C can finish the remaining work?

  1. 16

  2. 18

  3. 20

  4. 22

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

A's rate = 1/36 per day. In 12 days, A completes 12/36 = 1/3. Remaining = 2/3. B works 6 days at 1/24 per day = 6/24 = 1/4. Remaining = 2/3 - 1/4 = 5/12. C's rate = 1/48 per day. Time = (5/12) / (1/48) = (5/12) × 48 = 20 days.

Multiple choice

A and B can complete a piece of work in 20 days, B and C can do it in 30 days. A and C can do it in 40 days. What is the respective ratio of the number of days taken by A, B and C respectively when they complete the same work independently? A और B किसी कार्य को 20 दिनों में B और C उसी कार्य को 30 दिनों में एवं A और C उसी कार्य को 40 दिनों में पूरा कर सकते हैं। A, B और C के द्वारा लिये गये दिनों की संख्या में क्रमशः अनुपात क्या है, यदि वे अकेले - अकेले कार्य को पूरा करते हैं?

  1. 7 : 5 : 35

  2. 5 : 35 : 2

  3. 7 : 35 : 5

  4. 5 : 5 : 1
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let A, B, C be daily work rates. A+B = 1/20, B+C = 1/30, A+C = 1/40. Adding all: 2(A+B+C) = 1/20 + 1/30 + 1/40 = 13/120, so A+B+C = 13/240. Therefore A = 13/240 - 1/30 = 1/48, B = 13/240 - 1/40 = 1/35, C = 13/240 - 1/20 = 1/240. Days ratio (reciprocal): 48 : 35 : 240 = 7 : 5 : 35.

Multiple choice

A can do a piece of work in 24 days, while B alone can do it in 16 days. With the help of C, they finish the work in 8 days .C alone can do the work in - A एक कार्य 24 दिनों में कर सकता है, जबकि B अकेला उसी कार्य को 16 दिनों में कर सकता है। वे दोनों C के साथ मिलकर वह कार्य 8 दिनों में पूरा कर देते है। तद्नुसार, C अकेला उसे कितने दिनों में कर सकता है?

  1. 32 days/दिन

  2. 36 days/दिन

  3. 40 days/दिन

  4. 48 days/दिन
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Work rates: A = 1/24 per day, B = 1/16 per day. Combined (A+B+C) = 1/8 per day. So C's rate = (1/8) - (1/24 + 1/16) = (1/8) - (5/48) = (6/48 - 5/48) = 1/48 per day. Therefore C alone can complete the work in 48 days. This is a standard work and time problem using combined work rates.

Multiple choice

12 men can complete a piece of work in 36 days. 18 women can complete the same piece of work in 60 days. 8 men and 20 women work together for 20 days. If only women were to complete the remaining piece of work in 4 days, how many women would be required? 12 आदमी एक काम को 36 दिनों में पूरा कर सकते हैं | 18 महिलाएं उसी काम को 60 दिनों में पूरा कर सकते हैं | 8 आदमी और 20 महिलायें 20 दिनों तक साथ में काम करते हैं | यदि केवल महिलायें शेष काम को 4 दिनों में पूरा करती हैं, कितनी महिलाओं की आवश्यकता होगी ?

  1. 70

  2. 66

  3. 40

  4. 28
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

12 men in 36 days means 1 man does 1/(12×36) work per day. 18 women in 60 days means 1 woman does 1/(18×60) work per day. Work done by 8 men + 20 women in 20 days = 20×[8/432 + 20/1080] = 20×[0.0185 + 0.0185] = 20×0.037 = 0.74 work. Remaining work = 0.26. For women to complete 0.26 work in 4 days: W × (1/1080) × 4 = 0.26, so W = 0.26×1080/4 = 70 women. The key is finding individual work rates, then calculating remaining work.

Multiple choice

Twenty women together can complete a work in 16 days. 16 men together can complete the same work in 15 days. The ratio of the working capacity of a woman to that of a man is - 20 औरतें एक काम को 16 दिनों में पूरा कर सकती हैं। 16 आदमी उसी काम को 15 दिनों में पूरा कर सकते हैं। एक महिला और एक पुरुष की कार्यक्षमता में क्रमशः अनुपात है -

  1. 4 : 3

  2. 3 : 4

  3. 3 : 5

  4. 5 : 4
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

20 women complete work in 16 days, so 1 woman's rate = 1/(20×16) = 1/320 per day. 16 men complete same work in 15 days, so 1 man's rate = 1/(16×15) = 1/240 per day. Ratio woman:man = (1/320) : (1/240) = 240 : 320 = 3 : 4. The woman has 3/4 the working capacity of a man.

Multiple choice

A can do a work in 3 days. B can do the same work in 2 days. Both of them finish the work together and get Rs.150. What \% of share of B is more than share of A?

  1. 33(1/3)%

  2. 100%

  3. 50%

  4. 75%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Work efficiency: A does 1/3 work per day, B does 1/2 work per day. Ratio of efficiency A:B = 1/3:1/2 = 2:3. Wages are distributed in ratio of work done, so A gets Rs.60 (40%) and B gets Rs.90 (60%). B's share is (90-60)/60 × 100 = 50% more than A's share.

Multiple choice

A, B and C can complete a work in 30 days by working together. If the efficiency of A and C are twice the efficiency of B and the efficiency of A and B is thrice the efficiency of C. In how many days A will complete the work? A, B और C एक साथ कार्य करके किसी कार्य को 30 दिनों में पूरा कर सकते हैं । यदि A और C की कार्यक्षमता B की कार्यक्षमता की दुगनी है और A और B की कार्यक्षमता C की कार्यक्षमता की तीन गुनी है, तो A काम को कितने दिनों में समाप्त कर लेगा ?

  1. 72 days/दिन

  2. 40 days/दिन

  3. 30 days/दिन

  4. 20 days/दिन
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let A, B, C have efficiencies a, b, c. Combined rate: a + b + c = 1/30 work/day. Given: a + c = 2b and a + b = 3c. Substituting: a + c = 2b means a + c + b = 3b, so 1/30 = 3b, giving b = 1/90. From a + b = 3c: a + 1/90 = 3c. Also a = 2b - c = 2/90 - c. Solving gives a = 1/72, so A takes 72 days alone. Option B (40 days) is incorrect. Option C (30 days) is the combined time, not A's alone. Option D is a miscalculation.

Multiple choice

Prasad is thrice as good a workman Malviya and therefore able to finish a work in 48 days less than Malviya. Working together, they can do it in प्रसाद एक कारीगर मालवीय से तीन गुना कुशल है और इसलिए एक काम को मालवीय से 48 दिन कम में काम समाप्त कर देता है | एक साथ काम करके, वे इसे कर सकते हैं

  1. 18 days/दिन

  2. 24 days/दिन

  3. 30 days/दिन

  4. 12 days/दिन
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let Malviya alone finish the work in x days. Since Prasad is thrice as good (efficient), Prasad finishes in x/3 days. Given that Prasad takes 48 days less than Malviya: x - x/3 = 48, so 2x/3 = 48, giving x = 72 days. So Malviya takes 72 days alone, and Prasad takes 24 days alone. Working together, their combined rate is 1/72 + 1/24 = 1/72 + 3/72 = 4/72 = 1/18, meaning they finish in 18 days together. The key is setting up the equation correctly based on relative efficiency.

Multiple choice

2 men and 3 women finish 25 % of the work in 8 days . 6 men and 12 boys finish the 20% of the work in 4 days .In how many days can 8 men and 3 women and 12 boys finish 40% of the work together.(in approx.) 2 आदमी 3 महिलाएं 25 % कार्य 8 दिनों में पूरा करती हैं | 6 आदमी और 12 लड़के 20 % कार्य 4 दिन में पूरा करते है | 8 आदमी और 3 महिलाएं और 12 लड़के 40% कार्य को कितने दिन में कर सकता है |(लगभग में )

  1. 2

  2. 5

  3. 7

  4. 9
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let m, w, b be work per day by man, woman, boy. From (1): 2m + 3w = 0.25W/8 = W/32. From (2): 6m + 12b = 0.2W/4 = W/20. From (1) and (2), if m = w, then 5m = W/32, so m = W/160. Then 6(W/160) + 12b = W/20, giving b = W/120. For 40% work: (8m + 3w + 12b) × days = 0.4W. Substituting: (11m + 12b) = 11(W/160) + 12(W/120) = 11W/160 + W/10 = 27W/160. Days = 0.4W / (27W/160) = 64/27 ≈ 2.37 days. But answer is 5, suggesting different work rate assumptions.