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

In how many days will 5 men and 4 women together complete the work?\newline\textbf{(I).} 15 men and 12 women can complete the same work in 12 days.\newline\textbf{(II).} 10 men and 8 women can complete the same work in 16 days.

  1. Only II

  2. Only I

  3. From I and II

  4. Either from I or II

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

Let m and w be the work done by 1 man and 1 woman per day. From statement I: 15m + 12w = 1/12, which simplifies to 5m + 4w = 1/36. This means 5 men and 4 women complete 1/36 of the work daily, so they need 36 days total. From statement II: 10m + 8w = 1/16, which simplifies to 5m + 4w = 1/32, giving 32 days. Each statement alone gives us the value of 5m + 4w, which is exactly what we need to find the time for 5 men and 4 women.

Multiple choice

10 men and 15 women together can complete a work in 6 days. It takes 100 days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work? 10 पुरूषों और 15 महिलायें साथ में एक काम को 6 दिनों में पूरा कर सकते है। उसी काम को अकेले एक पुरूष 100 दिनों में पूरा कर सकता है तो उसी काम को अकेले एक महिला कितने दिनों में पूरा कर सकती है?

  1. 204 days/दिन

  2. 336 days/दिन

  3. 225 days/दिन

  4. 284 days/दिन
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

1 man's 1 day work = 1/100. 10 men and 15 women's 1 day work = 1/6. So 10(1/100) + 15(1/w) = 1/6. Therefore: 1/10 + 15/w = 1/6. 15/w = 1/6 - 1/10 = (5-3)/30 = 2/30 = 1/15. So w = 15 × 15 = 225 days. One woman alone takes 225 days.

Multiple choice

Pankaj and Abdul are two friends. A total of Rs. 900 was paid to both of them for completing a work. Pankaj started working and worked for ‘x’ days and then left and the remaining work was completed by Abdul and he was paid Rs. 540. If Pankaj and Abdul alone can complete the work in 15 days and Y days resp. Which of the following options is /are possible for the value of 'X' and 'Y' are respectively. A- 6 , 18 B- 6,30 C- 6, 25 D-8, 25

  1. Only A

  2. Both B and C

  3. A, B and C

  4. Only C

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

Pankaj and Abdul together receive Rs. 900 for a work. Pankaj works x days at rate 1/15 per day, Abdul completes the rest and receives Rs. 540. Pankaj gets Rs. 360. Abdul's payment being 1.5 times Pankaj's means he did 1.5 times the work: (1 - x/15) = 1.5(x/15), giving x = 6. With x = 6, Pankaj does 2/5 work, Abdul does 3/5 work in 10.8 days. Y = 18 works. Also if Y = 25, Abdul's rate = 1/25, Pankaj's = 1/37.5 (not 15). If Y = 30, Pankaj's = 1/45. The only valid pair from given options is x = 6, Y = 18, but the question asks which options are possible. Given the constraints, only option A (6, 18) is mathematically consistent.

Multiple choice

Four workers P,Q,R,S complete a work in different days and they individually take 12 days, 36 days , 24 days and 18 days but not in the same order. Their efficiencies are in descending order. If they start work together and after 1 day P left the work and next day Q left the work and next day S left the work, then in how many days R complete the remaining work and what is the ratio of completed work to remaining work after the day S left the work?

  1. 21 days 12 hours & 72:43

  2. 21 days 12 hours & 29:72

  3. 14 days 8 hours & 29:43

  4. 14 days 8 hours & 29:72

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

Workers take 12, 18, 24, 36 days individually. Since efficiencies are descending (most efficient = least days), P=12 days, Q=18 days, R=24 days, S=36 days. Combined work per day = 1/12 + 1/18 + 1/24 + 1/36 = 6/72 + 4/72 + 3/72 + 2/72 = 15/72 = 5/24. Day 1: All work = 5/24, then P leaves. Day 2: Q + R + S work = 1/18 + 1/24 + 1/36 = 4/72 + 3/72 + 2/72 = 9/72 = 1/8 = 3/24, total = 8/24, Q leaves. Day 3: R + S work = 1/24 + 1/36 = 3/72 + 2/72 = 5/72, total = 29/72, S leaves. Remaining work = 1 - 29/72 = 43/72. Ratio completed:remaining = 29:43. R alone does 1/24 per day, so for 43/72 work: (43/72) / (1/24) = (43/72) × 24 = 43/3 = 14 days and 8 hours.

Multiple choice

If A and B together can do a piece of work in 6 days and A alone can do the same piece of work in 8 days. Find the time taken by B to complete this work. यदि A और B एकसाथ मिलकर एक कार्य को 6 दिनों में कर सकते हैं और A अकेला उसी कार्य को 8 दिनों में कर सकता है | B द्वारा इस कार्य को पूरा करने में लिया गया समय ज्ञात कीजिये ।

  1. 12 days/दिन

  2. 10 days/दिन

  3. 24 days/दिन

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

Work rate problems: combined rate = sum of individual rates. A + B together: 1/6 work per day. A alone: 1/8 work per day. Therefore B's rate = (1/6 - 1/8) = (4/24 - 3/24) = 1/24 work per day. Time for B alone = 1/(1/24) = 24 days.

Multiple choice

A work can be finished in 20 days by some worker. Due to absence of 110 worker work completed in 30 days. Find the number of worker initially कुछ श्रमिक एक कार्य को 20 दिन में समाप्त करते हैं। 110 श्रमिक अनुपस्थित होते के कारण पूरा कार्य 30 दिनों में समाप्त हो जाता है। तो प्रारम्भ में श्रमिकों की संख्याा बताइए।

  1. 220

  2. 550

  3. 440

  4. 330
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Workers × Time = Constant. W × 20 = (W-110) × 30. Solving: 20W = 30W - 3300, so 10W = 3300, W = 330 workers.

Multiple choice

Ram alone can do a work in 20 days. Mohan is 25% more efficient than Ram. Ram and Mohan started working and worked for 4 days. If Sita alone completed the remaining job in 22 days. How many days Sita alone takes to complete the entire job?

  1. 24 days

  2. 36 days

  3. 12 days

  4. 20 days

  5. 40 days
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Ram's efficiency: 1/20 work per day. Mohan is 25% more efficient, so his rate = 1.25×(1/20) = 1/16 per day. In 4 days, Ram and Mohan complete: 4×(1/20 + 1/16) = 4×(4/80 + 5/80) = 4×(9/80) = 9/20 of work. Remaining work = 1 - 9/20 = 11/20. Sita completes 11/20 work in 22 days, so her rate = (11/20)/22 = 11/440 = 1/40 per day. Therefore, Sita alone takes 40 days to complete the entire job.

Multiple choice

The work done by a man, a woman and a child is in the ratio of 5: 3: 1. There are 20 men, 24 women and 40 children in a factory. Their weekly wages amount to ₹1484, which is divided in the ratio of work done by the men, women and children. What was the amount paid to 12 men, 20 women and 30 children in the February, 2017?

  1. Rs 3200

  2. Rs 10400

  3. Rs 4200

  4. Rs 3600

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

First calculate wage per unit: total wages ₹1484 divided by total work units (20×5 + 24×3 + 40×1 = 100 + 72 + 40 = 212) = ₹7 per unit. For 12 men, 20 women, 30 children: work units = 12×5 + 20×3 + 30×1 = 60 + 60 + 30 = 150 units. Amount = 150 × 7 = ₹1050. But this is weekly; for February 2017, we multiply by 4 weeks = ₹4200. The answer matches Option C.

Multiple choice

A can do a work in 15 days, B can do it in 12 days but C can do (\frac{3}{4})th of the work in 18 days. Find the time taken by all together to complete the whole work.
  1. $4(\frac{7}{15}) days$
  2. $5(\frac{5}{23}) days$
  3. $6(\frac{3}{19}) days$
  4. $4(\frac{13}{25}) days$

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

A's rate: 1/15 work/day. B's rate: 1/12 work/day. C does 3/4 work in 18 days, so full work in 24 days, rate = 1/24. Combined rate = 1/15 + 1/12 + 1/24 = 8/120 + 10/120 + 5/120 = 23/120. Time = 120/23 = 5(5/23) days.

Multiple choice

A man is 50% more efficient worker than a woman. A boy is 20% less efficient worker than a woman. What is share of a boy in wages of 3300 for a work if they are working together?

  1. 800

  2. 1500

  3. 1000

  4. 1200

  5. 1800
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let woman's efficiency be 100%. Then man's efficiency = 150% (50% more than woman) and boy's efficiency = 80% (20% less than woman). Total efficiency = 100 + 150 + 80 = 330%. Wages are distributed in proportion to efficiency. Boy's share = (80/330) × 3300 = 800. The boy's efficiency is 80/330 of total, so his wage is the same fraction of total wages.

Multiple choice

M and N can do a piece of work in 30 days, while N and O can do the same work in 24 days and O and M in 20 days. They all work together for 10 days till N and O leave. How many days more will M take to finish the work?

  1. 35

  2. 15

  3. 22

  4. 18

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

Let M, N, O's individual work rates be m, n, o work/day. M+N: 30 days, so m+n = 1/30. N+O: 24 days, so n+o = 1/24. O+M: 20 days, so o+m = 1/20. Adding all three: 2(m+n+o) = 1/30 + 1/24 + 1/20 = 1/8. So m+n+o = 1/16. In 10 days together, they complete 10/16 = 5/8 of work. Remaining work = 3/8. M's rate alone = (m+n+o) - (n+o) = 1/16 - 1/24 = 1/48. M needs (3/8)/(1/48) = 18 days.

Multiple choice

A work is assigned to some workers of a factory. If they start work on Tuesday and work continuously on every day of week the work lasts on Friday of same week. But when 5 workers left the group on every working day the work will complete on Monday of next week. How many workers were at the beginning?

  1. 40

  2. 35

  3. 30

  4. 70

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

Let initial workers = x. Work takes 4 days normally, so total work = x + (x-5) + (x-10) + (x-15) = 4x - 30. With attrition, takes 7 days: sum from first term to (x-30) = 7x - 105. Equating: 7x - 105 = 4(4x - 30). Solving gives x = 35.

Multiple choice

A certain number of men can complete a job in 30 days. If there were 5 men more, it could be completed in 10 days less. How many men were in the beginning? कुछ निश्चित आदमी किसी कार्य को 30 दिनों में कर सकते है. यदि 5 आदमी और होते तो कार्य 10 दिन पहले ख़त्म हो जाता । तो प्रारम्भ में कितने आदमी थे?

  1. 10

  2. 15

  3. 20

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

Let initial men = m, total work = W. Work done is constant: m×30 = (m+5)×20. So 30m = 20m + 100, giving 10m = 100, hence m = 10 men.

Multiple choice

A certain number of men can finish a work in 100 days. If however there were 10 men less, it would take another 10 days to finish the work. How many men were there originally? एक निश्चित संख्या में पुरुष 100 दिनों में एक काम पूरा कर सकते हैं। हालांकि अगर 10 आदमी कम थे, तो काम खत्म होने में 10 दिन और लगेंगे। मूल रूप से वहां कितने आदमी थे?

  1. 50

  2. 75

  3. 82

  4. 110
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let initial men = m. Work is constant: m×100 = (m-10)×110. So 100m = 110m - 1100, giving 10m = 1100, hence m = 110 men.