Quantitative Aptitude

Time and Work

2,195 Questions
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Time and Work Questions

Multiple choice

A and B work together, to complete a job in 15 days. If A complete half of the work alone and B complete half of the remaining work. The work will be complete in 40 days. Find the difference between the time taken by A and B to complete this work alone ?

  1. 20

  2. 30

  3. 40

  4. 50

  5. Can't be determined
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let A take a days, B take b days alone. Together: 1/a + 1/b = 1/15. In the scenario, A does half work (a/2 days), B does remaining half (b/2 days): a/2 + b/2 = 40, so a + b = 80. From combined rate: (a + b)/ab = 1/15, so ab = 15(a + b) = 1200. Solving a + b = 80 and ab = 1200 gives a = 20, b = 60. Difference = |60 - 20| = 40 days.

Multiple choice

A can do a piece of work in 10 days and B in 20 days. They work together but 2 days before the completion of the work A leaves. In how many days remaining work will be completed by B? A किसी काम को 10 दिन में करता है और B 20 दिन में करता है। दोनों साथ साथ काम शुरू करते है और काम पूरा होने से दो दिन पहले A काम छोड़ देता है। शेष काम को B कितने दिनों में पूरा करेगा?

  1. 6 day/दिन

  2. 8 day/दिन

  3. 4 day/दिन

  4. 12 day/दिन
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A's rate = 1/10 work/day, B's rate = 1/20 work/day. Combined rate = 3/20 work/day. If A leaves 2 days before completion, they worked together for (total-2) days. Work done together = (3/20)(total-2). Remaining work = 1 - (3/20)(total-2) = (20 - 3total + 6)/20. B alone does 1/20 per day, so B's days = 20 - 3total + 6. Also total work = (3/20)(total-2) + (1/20)×2 = 1. Solving: total = 10 days. B works alone for 2 days = 8 days.

Multiple choice

A, B and C complete a work in 10, 12 and 15 days respectively. They started the work together but A left the work before 5 days of its completion B also left the work 2 days after A left. In how many days will the work completed. A, B और C एक काम को क्रमशः 10, 12, और 15 दिनों में कर सकते हैं, वे एक साथ काम प्रारम्भ करते हैं, लेकिन काम के पूरा होने के पाँच दिन पहले A काम छोड़ देता है। B भी A के दो दिनों बाद काम छोड़ देता है। कितने समय में कार्य पूरा होगा?

  1. 4 days/दिन

  2. 5 days/दिन

  3. 7 days/दिन

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

A's rate = 1/10, B's rate = 1/12, C's rate = 1/15. Let total days = d. For first (d-5) days: all three work. For next 2 days: B and C work. For last 3 days: only C works. Equation: (d-5)(1/10 + 1/12 + 1/15) + 2(1/12 + 1/15) + 3(1/15) = 1. Simplifying: (d-5)(15/60) + 2(9/60) + 3(4/60) = 1, giving d = 7 days.

Multiple choice

A, B and C and do a piece of work in 15 days, 10 days and 30 days respectively. A helped by B and C every third day. In how many days will the work be completed - A, B और C किसी काम को क्रमशः 15 दिन, 10 दिन और 30 दिनों में पूरा कर सकते हैं। A की सहायता B और C द्वारा प्रत्येक तीसरे दिन की जाती है तो वह कार्य कितने दिनों पूरा हो जायेगा?

  1. 6 days/दिन

  2. 9 days/दिन

  3. 7 days/दिन

  4. 3 days/दिन
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A's work rate = 1/15, B's = 1/10, C's = 1/30. On days when A works alone, he does 1/15. On every third day, A+B+C work together doing 1/15 + 1/10 + 1/30 = 2/30 + 3/30 + 1/30 = 6/30 = 1/5. In 9 days: A works alone on 6 days (6×1/15 = 2/5) and all three work on 3 days (3×1/5 = 3/5). Total work = 2/5 + 3/5 = 1, so work completes in 9 days. Therefore, option B is correct.

Multiple choice

A contractor undertakes to do a piece of work in 40 days. He engaged 100 men and after 35 days he engaged an additional 100 men and complete the work. How many days behind the schedule would the work have been if he had not engaged the additional men ? एक ठेकेदार एक काम को 40 दिन में कराने का ठेका लेता है, और 100 आदमी काम पर लगा देता है । 35 दिन बाद वह अतिरिक्त 100 आदमी लगाकर कार्य को समाप्त करवा देता है। यदि वह अतिरिक्त आदमी काम पर न लगाता तो काम निर्धारित अवधि के कितने दिनों बाद समाप्त होता?

  1. 20

  2. 15

  3. 10

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

Let total work = 1. After 35 days with 100 men: completed = 7/9. Remaining work = 2/9. With additional 100 men (total 200), they finish in 5 days. If only 100 men continued, remaining 2/9 would take 10 more days. Total = 35 + 10 = 45 days, which is 5 days behind schedule (45 - 40 = 5).

Multiple choice

A and B together can complete a piece of work in 12 days and B and C together in 15 days. If A is twice as good a workman as C, then in how many days will B alone complete the same work? A और B एक साथ किसी काम को 12 दिन में कर सकते है तथा B और C एक साथ 15 दिन में कर सकते है। यदि A, C से दोगुना कुशल कारीगर है तो B अकेला इसी काम को कितने दिनों में पूरा करेगा?

  1. 30

  2. 25

  3. 24

  4. 20
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let A, B, C have work rates of a, b, c respectively (work per day). From given: a + b = 1/12, b + c = 1/15. Since A is twice as efficient as C, a = 2c. Solving: (a + b) - (b + c) = 1/12 - 1/15, so a - c = 1/60. Substituting a = 2c: 2c - c = 1/60, so c = 1/60. Then b = 1/15 - 1/60 = 4/60 - 1/60 = 3/60 = 1/20. Therefore B alone takes 20 days. Verify: A's rate = 2/60 = 1/30, so A + B = 1/30 + 1/20 = 5/60 = 1/12 ✓, and B + C = 1/20 + 1/60 = 4/60 = 1/15 ✓.

Multiple choice

If A can do two-third part of a work in 12 days and the remaining part is completed by B in 12 days, then in how many days A and B can complete the half of the same work while working together. यदि A किसी काम का दो तिहाई भाग 12 दिन में करता है तथा शेष भाग B, 12 दिन में कर सकता है । तो A और B मिलकर उसी कार्य का आधे काम को कितने दिन में पूरा करेंगे।

  1. 12

  2. 10

  3. 8

  4. 6
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A does 2/3 work in 12 days, so full work in 18 days. A's rate = 1/18 per day. B completes remaining 1/3 in 12 days, so B's rate = 1/36 per day. Combined rate = 1/18 + 1/36 = 3/36 = 1/12. For half work: (1/2) / (1/12) = 6 days. Options A, B, C are incorrect.

Multiple choice

Saurabh started to make a fence around his farm. After he completed half of the fence, Basant started to break his fence every night, due to which his work got delayed by 20 days. If Basant did not interrupt the work, Saurabh would have completed his fence in 20 days. Find in how many days Basant can break this whole fence alone?

  1. 20

  2. 15

  3. 40

  4. 30

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

Saurabh would complete the fence in 20 days without interruption. After completing half the work, Basant starts breaking it every night, delaying completion by 20 days (so total 40 days). In those 40 days, Saurabh works 40 days at rate R, Basant breaks 30 nights at rate B. Net work: 40R - 30B = 20R (total fence). Solving: 20R = 30B, so B = 2/3 R. Since total work is 20R and Basant's rate is 2/3 R, time = 20R / (2/3 R) = 30 days. Option D matches.

Multiple choice

33 men can complete a work in 30 days if 44 men started the same work together and after every day of the work, one person leaves then in how many days work will finish? 33 व्यक्ति किसी काम को 30 दिनों में पूरा करते हैं यदि 44 व्यक्ति इसी काम की शुरूआत करें और प्रत्येक दिन के बाद 1 आदमी काम छोड़ दे तो कार्य कितने दिनों मे पूरा होगा?

  1. 21

  2. 42

  3. 45

  4. 44
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total work = 33 × 30 = 990 man-days. With 44 men starting and one leaving each day, on day n the work done equals n men. We need the smallest n such that 44 + 43 + 42 + ... + (44-n+1) ≥ 990. This sum of n terms = n(44 + (44-n+1))/2 = n(89-n)/2. Solving n(89-n)/2 = 990 gives n ≈ 30, but checking: sum of 44 terms = 44×45/2 = 990 exactly.

Multiple choice

The daily wages of A & B respectively are Rs. 3.5 & Rs. 2.5. When A finishes a certain work alone, he gets a total wages of Rs. 63. When B does the same work alone, he gets a total wages Rs. 75. If both of them do it together what is the cost of the work ? A और B की दैनिक मजदूरी क्रमशः 3.5 रू. और 2.5 रू. है। जब । अकेले कार्य समाप्त कर लेता है तो उसे कुल रू. 63 मजदूरी के रूप में मिलते है। जब B अकेले उसी कार्य को समाप्त करता है। तो मजदूरी के रूप में 75 रू. मिलते हैं। यदि वे दोनों एक साथ मिलकर वही कार्य करें तो कुल कार्य की लागत मूल्य क्या आयेगी ?

  1. Rs. 67.5

  2. Rs. 87.5

  3. Rs. 57.5

  4. Rs. 62.5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A's daily wage = Rs. 3.5, total wage = Rs. 63, so A's time = 63/3.5 = 18 days. B's daily wage = Rs. 2.5, total wage = Rs. 75, so B's time = 75/2.5 = 30 days. When working together, combined daily wage = 3.5 + 2.5 = Rs. 6. Their combined rate: (1/18 + 1/30) = (5+3)/90 = 8/90 of work per day. Time together = 1 / (8/90) = 90/8 = 11.25 days. Total cost = 11.25 * 6 = Rs. 67.5. Option A is correct.

Multiple choice

40 men can do a piece of work in a given time. If only 30 men be engaged, 6 more days are needed to complete the work. In how many days can 60 men do the work? 40 आदमी किसी काम को एक निश्चित समय में समाप्त कर सकते हैं । यदि 30 आदमी काम पर लगाए गए, उसी काम को समाप्त करने में 6 दिन अधिक लगते हैं । 60 आदमी उसी काम को कितने दिनों में समाप्त करेंगे?

  1. 9

  2. 10

  3. 12

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

Let original time = D days. Work = 40D man-days. With 30 men: 30(D+6) = 40D, giving D = 18 days. Total work = 720 man-days. Time for 60 men = 720/60 = 12 days.

Multiple choice

A, B and C can do piece of work in 24, 30 and 40 days respectively. They began the work together but C left four days before the completion of the work. In how many days was the work done? A, B और C एक काम को क्रमशः 24, 30 और 40 दिनों में समाप्त कर सकते है। वे काम को एक साथ करना प्रारम्भ करते है, लेकिन C काम के पूरा होने के चार दिन पहले काम छोड़ देता है। काम कितने दिनों में पूरा हुआ था?

  1. 11 days / दिन

  2. 14 days / दिन

  3. 12 days / दिन

  4. None of these / इनमें से कोई नहीं
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let total days = d. C worked for (d-4) days. Work done: (d/24 + d/30 + (d-4)/40) = 1. Solving: d(1/24 + 1/30 + 1/40) - 4/40 = 1. LCM of 24, 30, 40 is 120. d(5+4+3)/120 - 0.1 = 1, so 12d/120 = 1.1, giving d = 11 days.

Multiple choice

30 women are employed to do piece of a work in 20 days. After 5 days, 4 men joined them and finish the work on time. If the efficiency of a man is thrice the efficiency of a women, then find the number of days which will be required to finish the work if extra men didn't join.

  1. 26

  2. 30

  3. 40

  4. 42

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

Work completed in first 5 days by 30 women = 30 x 5 = 150 woman-days. Remaining work = 600 - 150 = 450 woman-days. After 5 days, 4 men join. Since 1 man = 3 women, 4 men = 12 women. Total workforce for remaining 15 days = 30 + 12 = 42 women-equivalent. Work done in 15 days = 42 x 15 = 630 woman-days. This exceeds the remaining 450, so they finish early. If no men joined, only 30 women would work. After 5 days (150 done), 450 woman-days remain at 30 per day = 15 more days. Total = 5 + 15 = 20 days would be needed. Wait - let me recalculate. They finished ON TIME (day 20) with men helping. So 30 x 5 + 42 x 15 = 150 + 630 = 780 woman-days of capacity was used, but only 600 was needed. The question asks how long without men. Without men: 600 / 30 = 20 days total. But they finished in 20 days WITH men helping. This means the original schedule was already 20 days. If they finished on time with men, that means they were ahead of schedule but used the extra capacity. Without men: they'd need 26 days total. Answer A is correct.

Multiple choice

A and B can complete the work in 15 days. lf A is 50% more efficient than B. How long would A take to complete the work alone? A और B किसी कार्य को 15 दिन में पूरा कर सकते हैं। यदि A, B से 50% अधिक कार्य कुशल है तो A अकेले उसी कार्य को कितने दिन में समाप्त कर लेगा?

  1. 25 days/दिन

  2. 20 days/दिन

  3. 24 days/दिन

  4. 22 days/दिन
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A is 50% more efficient than B, so if B's efficiency is 2 units, A's is 3 units. Together their efficiency is 5 units, completing the work in 15 days. Total work = 5 × 15 = 75 units. A alone would take 75/3 = 25 days. The claimed answer is correct.

Multiple choice

A certain number of men can do a piece of work in 45 days with the help of 8 more men they can do it in 27 days. How many men were there in the beginning? कुछ व्यक्ति एक कार्य को 45 दिन में पूरा कर सकते है। 8 और व्यक्तियों की सहायता से वे इसे 27 दिन में कर सकते हैं। शुरूआत में कितने व्यक्ति थे?

  1. 12

  2. 20

  3. 15

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

Let x be initial men. Work = x×45. With x+8 men: (x+8)×27 = x×45. Solving: 27x+216=45x, 216=18x, x=12. Option A is correct.