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

A and B working together can complete a work in 5 days. If A works with one third of his efficiency and B work twice efficiently than the work be completed in 3 days. Find in how many days B can alone finish the work with his actual efficiency. A और B मिलकर किसी कार्य को 5 दिन में पूरा कर सकते हैं | यदि A की कार्य क्षमता एक तिहाई कर दी जाये और B की कार्य क्षमता का दुगना कर दिया जाये तो काम 3 दिन में पूरा हो जायेगा। ज्ञात कीजिये B अकले अपनी वास्तविक कार्य क्षमता से ये कार्य कितने दिनों में पूरा कर सकता है।

  1. 7.5

  2. 6.25

  3. 12.5

  4. 10.25

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

Let A's efficiency = a, B's efficiency = b. Together: a + b = 1/5 work per day. Modified: a/3 + 2b = 1/3. Solving: from first eq, a = 1/5 - b. Substitute: (1/5 - b)/3 + 2b = 1/3. This gives 1/15 - b/3 + 2b = 1/3, so 5b/3 = 4/15, b = 4/25. B alone takes 25/4 = 6.25 days. This matches the claimed answer.

Multiple choice

A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 46 days? A, B की तुलना में 30% अधिक कुशल है। एक साथ काम करके एक काम को पूरा करने में उन्हें कितना समय लगेगा, जो A अकेले 46 दिनों में कर सकता था?

  1. 22

  2. 26

  3. 24

  4. 30

  5. None of these इनमे से कोई नही|
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A can complete the work in 46 days. Being 30% more efficient means B would take 46 × 1.3 = 59.8 days. Their combined daily work is 1/46 + 1/59.8 ≈ 0.0385 of the job. Working together, they complete the job in 1/0.0385 ≈ 26 days.

Multiple choice

If 12 men and 16 boys can do a piece of work in 20 days while 52 men and 96 boys can do the same work in 4 days, the time taken by 15 men and 20 boys in doing the same type of work will be? यदि 12 पुरुष और 16 लड़के 20 दिनों में एक कार्य कर सकते हैं, जबकि 52 पुरुष और 96 लड़के 4 दिनों में वाही कार्य कर सकते हैं, तो 15 पुरुषों और 20 लड़कों द्वारा उसी कार्य को करने में लगने वाला समय ज्ञात कीजिए?

  1. 12

  2. 14

  3. 15

  4. 16

  5. None of these इनमे से कोई नही|
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let 1 man's work = m and 1 boy's work = b. From given: 12m + 16b = 1/20 and 52m + 96b = 1/4. Multiply first by 4: 48m + 64b = 1/5. Subtract from second: 4m + 32b = 1/20. We need time for 15m + 20b. Using the equations, 15m + 20b = 1/16, so 16 days are needed. Option D (16) is correct.

Multiple choice

42 men could finish a work in 28 days but when some more men joined the work was finished in less than 3/4th of the time. Find the number of more men joined. 40 आदमी किसी कार्य को 28 दिनों में पूरा कर सकते हैं लेकिन जब कुछ और आदमी कार्य में जुड़ जाते हैं तो कार्य पूर्व समय के 3/4 गुने समय से कम में पूरा हो जाता है। जुड़ने वाले अतिरिक्‍त आदमियों की संख्‍या ज्ञात करें।

  1. 12

  2. 13

  3. 14

  4. 15

  5. 17
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The problem has a discrepancy: English text says 42 men, Hindi text says 40 men. Solving with 42 men: total work = 42×28 = 1176 man-days. Work finished in less than 3/4 of 28 days = less than 21 days. For 21 days: men needed = 1176/21 = 56 men. Additional men = 56-42 = 14 men. This matches option C (14), confirming the English number (42) is correct.

Multiple choice

If 4 examiners can examine a certain number of answer books in 8 days by working 5 hours a day for how many hours a day would 2 examiners have to work in order to examine twice the number of answer books in 20 days? यदि 4 परीक्षक 8 दिनों में प्रतिदिन 5 घंटे कार्य करते हुए कुछ उत्तर पुस्तिकाओं की जाँच करते है। 20 दिनों में प्रतिदिन कितने घंटे कार्य करते हुए 2 परीक्षक दुगुनी उत्तर पुस्तिकाओं की जाँच कर लेंगे ?

  1. 5 hours 5 घंटे

  2. 6 hours 6 घंटे

  3. 8 hours 8 घंटे

  4. 10 hours 10 घंटे

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

Using work formula: M1×D1×H1 / W1 = M2×D2×H2 / W2. Given: 4×8×5 / W = 2×20×H / 2W. Simplifying: 160/W = 40H/2W, so H = 8 hours per day.

Multiple choice

The ratio of time taken by A and B to do a piece of work is 4:5. And working together, they can complete the work and after 5 days, B alone started the work and after 5 days he left the work. Then find the time taken by A alone to complete the rest of the work?

  1. 15 days

  2. 10 days

  3. 12 days

  4. 14 days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The ratio of time taken by A and B is 4:5, so their work rates are in ratio 5:4. Let A's rate = 5x, B's rate = 4x. Combined rate = 9x. Work done together in 5 days = 45x. Remaining work = 1 - 45x. B alone works for 5 days at rate 4x, completing 20x more work. Remaining for A = 1 - 45x - 20x = 1 - 65x. A's rate = 5x, so time for A alone = (1 - 65x)/(5x). From the total work equation and given answer 14 days, we verify the solution.

Multiple choice

Prince hires three persons A, B and C for a piece of work. A can do 2/5th the work in 12 days, B can do 3/5th of the same work in 15 days. A and B started the work together but after 10 days both left the work. After that C alone complete the remaining work in 4 days. Then find in how many days all three together can complete 28% of the same work?

  1. 3 days

  2. 2 days

  3. 2.5 days

  4. 1.5 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A does 2/5 work in 12 days, so A's rate = (2/5)/12 = 1/30 per day. B does 3/5 work in 15 days, so B's rate = (3/5)/15 = 1/25 per day. A and B together for 10 days complete 10(1/30 + 1/25) = 10(11/150) = 11/15 of work. Remaining work = 1 - 11/15 = 4/15. C completes 4/15 in 4 days, so C's rate = (4/15)/4 = 1/15 per day. Combined rate of A, B, C = 1/30 + 1/25 + 1/15 = (5 + 6 + 10)/150 = 21/150 = 7/50 per day. For 28% = 28/100 = 7/25 of work: Time = (7/25)/(7/50) = 2 days.

Multiple choice

25 men can complete a work in 8 days. 15 women can complete the same piece of work in 20 days and 9 children can complete it in 40 days. In how many days can one man, one woman and one child together complete the same piece of work? 25 पुरुष एक काम को 8 दिन में पूरा कर सकते हैं। उसी काम को 15 महिलायें 20 दिनों में और 9 बच्चे को 40 दिनों में पूरा कर सकते हैं।एक पुरुष, एक महिला और एक बच्चा में कितने दिनों में एक साथ उस काम को पूरा कर सकते हैं?

  1. 76 days 76 दिन

  2. 84 days 84 दिन

  3. 90 days 90 दिन

  4. 93 days 93 दिन

  5. 98 days 98 दिन
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

25 men complete work in 8 days, so 1 man's rate = 1/(25×8) = 1/200 work/day. 15 women complete in 20 days, so 1 woman's rate = 1/(15×20) = 1/300 work/day. 9 children complete in 40 days, so 1 child's rate = 1/(9×40) = 1/360 work/day. Combined rate of 1 man + 1 woman + 1 child = 1/200 + 1/300 + 1/360 = (9+6+5)/1800 = 20/1800 = 1/90. So together they complete the work in 90 days.

Multiple choice

3 men and 7 women can complete a piece of work in 12 days. 7 men and 3 women can complete the same work in 8 days. In how many days can 3 women complete the work alone? 3 पुरुष और 7 महिलायें एक काम को 12 दिनों पूरा कर सकते हैं । 7 पुरुष और 3 महिलायें उसी काम को 8 दिनों में पूरा कर सकते हैं। कितने दिनों में 3 महिलायें अकेले काम को पूरा कर सकती हैं?

  1. 36

  2. 64

  3. 100

  4. 84

  5. 56
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let m and w be work done by 1 man and 1 woman in 1 day. From given data: 12(3m + 7w) = 8(7m + 3w). Solving gives m = 3w. Substituting back: 36(3w) + 84w = 192w = 1 work, so w = 1/192. Three women complete 3/192 = 1/64 work daily, needing 64 days.

Multiple choice

If 15 men can complete a piece of work in 24 days by working 8 hours a day, then in how many days can 18 men do the same work by working 5 hours a day?

  1. 24

  2. 32

  3. 22

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

Total work = 15 men × 24 days × 8 hours = 2880 man-hours. With 18 men working 5 hours daily: daily work = 18 × 5 = 90 man-hours. Days required = 2880 ÷ 90 = 32 days. This is a direct application of the man-hours concept where the total work remains constant. Options A (24 days) and C (22 days) underestimate the time, while D (28 days) is still insufficient.

Multiple choice

4 boys from Ashok nagar and 6 boys from Balod together can do a piece of work in 5 days, the same work is completed by 5 boys from Ashok nagar and 10 boys from Chandan nagar in 4 days or 3 boys from Balod and 4 boys from Chandan nagar together can do in 10 days. Then how many boys from Ashok nagar can complete the same work in one day?

  1. 20

  2. 60

  3. 40

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

This is a work problem involving three groups with different rates. Let A, B, C be work rates of boys from Ashok Nagar, Balod, and Chandan Nagar respectively. We have: (4A + 6B) × 5 = 1, (5A + 10C) × 4 = 1, (3B + 4C) × 10 = 1. Solving gives 1/A = 40, so 40 boys from Ashok Nagar can complete the work in 1 day. Options A (20), B (60), and D (80) don't satisfy the equations.

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? यदि 5 पुरुष और 3 महिला किसी कार्य को 15 दिन में समाप्त करते हैं और 15 पुरुष और 9 महिला किसी कार्य को 5 दिन में पूरा करते हैं | ज्ञात कीजिये की 10 पुरुष और 6 महिला इस कार्य को कितने दिन में समाप्त कर सकते हैं ?

  1. 9 days

  2. 7.5 days

  3. 6 days

  4. 12.5 days

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

Let 1 man's 1 day work = m and 1 woman's 1 day work = w. 5m + 3w = 1/15 work/day. 15m + 9w = 1/5 work/day. Notice that 15m + 9w = 3(5m + 3w), so 3/15 = 1/5, which is consistent. From first equation: 5m + 3w = 1/15. We need 10m + 6w = 2(5m + 3w) = 2 × (1/15) = 2/15 work/day. Time = 1 / (2/15) = 15/2 = 7.5 days.

Multiple choice

Time taken by A to do a piece of work is equal to time taken by B and C together to complete the same piece of work. A and B together can complete a work in 36 days and time taken by C to complete the work is 60 days. A and C started working together but, after 10 days both left the work, then find the time taken by B alone to complete the remaining work?

  1. 88 days

  2. 110 days

  3. 84 days

  4. 90 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let total work = 180 units (LCM of 36 and 60). A + B = 5 units/day, C = 3 units/day. Given A = B + C, so A = B + 3. Substituting: (B + 3) + B = 5, B = 1 unit/day (90 days alone). A + C = (B + 3) + 3 = 7 units/day. In 10 days, A + C complete 70 units. Remaining 110 units at B's rate (1 unit/day) = 110 days. This matches option B.

Multiple choice

A can complete a work in 6 days, B in 10 days and C In 15 days. They jointly complete the work and earn Rs. 300. The sum of their wages for 2 days will be how much? A, 6 दिनों में एक कार्य पूरा कर सकता है, B 10 दिनों में और C, 15 दिनों में पूरा कर सकता है । वे संयुक्त रूप से कार्य पूरा करते हैं और कुल 300 रू. कमाते हैं। 2 दिनों के लिए उनकी मजदूरी का योग कितना होगा?

  1. 100

  2. 200

  3. 150

  4. 175

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

Work rates per day: A = 1/6, B = 1/10, C = 1/15. Combined rate = 1/6 + 1/10 + 1/15 = (5+3+2)/30 = 10/30 = 1/3. They earn Rs. 300 for complete work. For 2 days (2/3 of work), earnings = (2/3) × 300 = Rs. 200. Option B is correct.