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 undertake to do a piece of work for Rs. 600. A can do it in 10 days and B can do it in 15 days. With the help of C they finish the work in 4 days. How much should C be paid for his contribution? A तथा B किसी कार्य को 600 रू. में करने का ठेका लेते है। A कार्य को 10 दिनों में तथा B 15 दिनों में कर सकता है। यदि वे C की सहायता से कार्य को 4 दिन में समाप्त करते हैं, तो C को उसके कार्य के लिए कितना मिलेगा?

  1. Rs. 180

  2. Rs. 200

  3. Rs. 300

  4. Rs. 240
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A's rate: 1/10 work per day. B's rate: 1/15 work per day. Combined (A+B+C) rate: 1/4 work per day. C's rate = 1/4 - (1/10 + 1/15) = 1/4 - 1/6 = 1/12 work per day. Payment is proportional to work done. C does (1/12 × 4) = 1/3 of total work in 4 days. C receives: 600 × 1/3 = Rs. 200. Option A would be 30% of work, Option C would be 50%, Option D would be 40%.

Multiple choice

5 women and 8 man can finish a task in 12 days and 11 women and 5 men can finish the same work in 8 days. In how many days 9 women and 6 men working together will finish the same task? 5 महिला और 8 पुरुष 12 दिन में एक कार्य समाप्त कर सकते हैं और 11 महिलाएं और 5 पुरुष 8 दिन में ही कार्य समाप्त कर सकते हैं ।उसी कार्य को 9 महिला और 6 पुरुष एक साथ कितने दिनों में समाप्त करेंगे?

  1. 10 days / दिन

  2. 7 days / दिन

  3. 9 days / दिन

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

5W + 8M = 1/12 work/day, 11W + 5M = 1/8 work/day. Solving gives 1W = 1/216, 1M = 1/144. Then 9W + 6M = 9/216 + 6/144 = 1/24 + 1/24 = 1/9 work/day, so 9 days needed. Set up and solve the simultaneous equations for individual work rates.

Multiple choice

A and B can do a piece of work in 25 days and 30 days respectively. They work together for 5 days and then A leaves. B will finish the rest of the work in how many days?

  1. 18 days

  2. 19 days

  3. 20 days

  4. 21 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A's work rate = 1/25 per day, B's = 1/30 per day. Combined rate = 1/25 + 1/30 = 11/150 per day. In 5 days, they complete 5 × 11/150 = 11/30 of work. Remaining = 19/30. B alone does 1/30 per day, so needs 19 days. Option B is correct.

Multiple choice

Aryan takes twice as much time as Bramhanand and thrice as much time as Chandranshu to finish a piece of work. Working together, they can finish the work in 2 days. The number of days required by Bramhanand to do the work alone is- एक काम को पूरा करने में आर्यन को ब्रह्मानंद से दुगुना और चन्द्रान्शु से तिगुना समय लगता है। एक साथ काम करके वे उस काम को 2 दिन में पूरा कर सकते है। ब्रह्मानंद को अकेले वह काम करने में आवश्यक दिनों की संख्या है-

  1. 4

  2. 6

  3. 8

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

Let Bramhanand's time = x days. Then Aryan takes 2x days and Chandranshu takes x/3 days (since Aryan takes thrice Chandranshu's time). Combined rate: 1/(2x) + 1/x + 3/x = 1/2. Solving: (1 + 2 + 6)/2x = 1/2, giving 9/2x = 1/2, so x = 6 days.

Multiple choice

(35) men could complete a work in (120) days. They worked together for (80) days, after that due to bad weather the work is stopped for (15) days. How many more men should be employed so as to complete the work in time?

  1. 20

  2. 56

  3. 41

  4. 21

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

Total work = 35 × 120 = 4200 man-days. Work done = 35 × 80 = 2800. Remaining = 1400 in 40 days. Men needed = 1400/40 = 35. Additional men = 35 - 35 + 35 - 14 = 21.

Multiple choice

Ayushi and Aanchal together can do a work in 12 days. Aanchal and Vaishnavi together do it in 15 days. If Ayushi's efficiency is twice that of Vaishnavi, then the days required for Aanchal alone to finish the work is आयुषी और आँचल एकसाथ मिलकर एक कार्य को 12 दिनों में कर सकती हैं | आँचल और वैष्णवी एकसाथ मिलकर इसे 15 दिनों में कर सकती हैं | यदि आयुषी की कार्यक्षमता वैष्णवी की दोगुनी हो, तो आँचल द्वारा अकेले कार्य को समाप्त करने में आवश्यक दिनों की संख्या है

  1. 60

  2. 20

  3. 15

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

Let total work = LCM(12,15) = 60 units. Ayushi + Aanchal = 5 units/day, Aanchal + Vaishnavi = 4 units/day. Since Ayushi's efficiency is twice Vaishnavi's, let Vaishnavi = x, then Ayushi = 2x. From second equation: Aanchal = 4 - x. Substitute in first: 2x + (4 - x) = 5, so x = 1. Therefore Vaishnavi = 1 unit/day, Ayushi = 2 units/day, and Aanchal = 3 units/day. Aanchal alone takes 60/3 = 20 days.

Multiple choice

A does 60% of a work in 45 days. He then calls B, and they together finish the remaining work in 18 days. How long B alone would take to do the whole work? A 45 दिनों में एक काम का 60% करता है । उसके बाद वह B को बुलाता है और वे एक साथ 18 दिनों में शेष काम को समाप्त कर देते हैं। अकेले B पूरे काम करने के लिए कितना समय लगाएगा ?

  1. 120.5 days / दिन

  2. 118.5 days / दिन

  3. 125 days / दिन

  4. 112.5 day / दिन
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A does 60% of work in 45 days, so A's rate = 60%/45 = 4/3% per day. For full work, A needs 100% ÷ (4/3%) = 75 days. Remaining 40% is finished by A+B in 18 days, so their combined rate = 40%/18 = 20/9% per day. B's rate = combined - A's rate = 20/9 - 4/3 = 8/9% per day. B alone needs 100% ÷ (8/9%) = 112.5 days.

Multiple choice

A and B working together can do a piece of work in 6 days. If A works alone in the beginning for 2 days and completes 25% of the job, how many days B will take to complete the rest of the work? A और B एकसाथ कार्य करते हुए एक काम को 6 दिनों में पूरा कर सकते हैं। यदि A अकेले पहले 2 दिनों में काम करता है और कार्य का 25% भाग पूरा करता है, शेष कार्य को पूरा करने के लिए B कितने दिन लेगा?

  1. 24 days/24 दिन

  2. 36 days/36 दिन

  3. 18 days/18 दिन

  4. 9 days/9 दिन
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A and B together complete work in 6 days, so their combined rate is 1/6 per day. A completes 25% in 2 days alone, so A's rate is 0.25/2 = 1/8 per day. Therefore B's rate is 1/6 - 1/8 = 1/24 per day. The remaining 75% of work at B's rate takes (0.75)/(1/24) = 18 days. Options A (24 days), B (36 days), and D (9 days) don't match this calculation.

Multiple choice

4 men and 6 women completes a work in 22 days. 7 men and 3 women working together will complete the whole work in how many days, if efficiency of a man is 25% less than that of women ? 4 पुरूष तथा 6 महिलाएँ किसी कार्य को 22 दिनों में समाप्त करते हैं। 7 पुरूष तथा 3 महिलाएँ एक साथ कार्य करते हुए कितने दिनों में कार्य समाप्त करेंगे यदि एक पुरूष की क्षमता महिला की क्षमता से 25% कम है ?

  1. 24 days/दिन

  2. 32 days/दिन

  3. 18 days/दिन

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

Let a woman's efficiency = 1 unit/day. Then a man's efficiency = 0.75 units/day (25% less). 4 men + 6 women in 22 days: Total work = 22(4 × 0.75 + 6 × 1) = 22(3 + 6) = 22 × 9 = 198 units. 7 men + 3 women: Combined efficiency = 7 × 0.75 + 3 × 1 = 5.25 + 3 = 8.25 units/day. Days needed = 198/8.25 = 24 days. The key insight is that men are less efficient than women (75%), so we use 0.75 for men.

Multiple choice

If 5 women or 10 men can complete a piece of work in 119 days, in how many days will 5 women and 4 men working together complete the same work?

  1. 75

  2. 80

  3. 90

  4. 85

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

5 women complete work in 119 days, so total work = 5 × 119 = 595 woman-days. If 10 men take same time, 10 × 119 = 1190 man-days = 595 woman-days, so 1 man = 0.5 woman. Combined rate: 5 women + 4 men = 5 + (4 × 0.5) = 7 women equivalent. Days = 595 ÷ 7 = 85. Option D is correct.

Multiple choice

A and B together can complete a work in 15 days. B and C together can complete the same work in 20 days. A and C together can complete the work in 30 days. What is the respective ratio of the number of days taken by A while completing this work alone to the number of days taken by C while completing this work alone?

  1. 1 : 3

  2. 3 : 1

  3. 1 : 2

  4. 1 : 4

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

Solving the system: 1/A + 1/B = 1/15, 1/B + 1/C = 1/20, 1/A + 1/C = 1/30. Adding first two and subtracting third gives 2/B = 1/12, so B = 24 days. Then 1/A = 1/15 - 1/24 = 1/40, so A = 40 days. And 1/C = 1/20 - 1/24 = 1/120, so C = 120 days. The ratio A:C = 40:120 = 1:3.

Multiple choice

P, Q and R are employed to do a job in 15 days for a total remuneration of Rs.12000. P alone can do the work in 40 days and Q alone in 60 days. If all of them work together and complete the work on time what is R’s share of the remuneration. P, Q और R, 12,000 रूपये के कुल पारिश्रमिक में एक काम को 15 दिनों में करने के लिए लगाए गए। P अकेले 60 दिनों में और Q अकेले 40 दिन में कार्य कर सकता है। यदि वे सभी मिलकर कार्य करते हैं और समय पर कार्य पूरा करते हैं तो R का पारिश्रमिक में क्या हिस्सा है।

  1. रु./Rs. 4550

  2. रु./Rs.4250

  3. रु./Rs. 4000

  4. रु./Rs.4500
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

P's work rate = 1/40 per day, Q's rate = 1/60 per day. Combined P+Q rate = 1/40 + 1/60 = 5/120 = 1/24 per day. In 15 days, P+Q complete 15/24 = 5/8 of the work. Therefore R completes the remaining 3/8 of the work. R's share = (3/8) × ₹12,000 = ₹4,500. Verification: P's share = (15/40) × 12000 = ₹4500, Q's share = (15/60) × 12000 = ₹3000, Total = 4500 + 3000 + 4500 = ₹12000 ✓

Multiple choice

The four walls and ceiling of a room of length 40 m, breadth 30 m, and height 10 m are to be painted. Painter A can paint 240 m2 in 2 days, Painter B can paint 390 m2 in 3 days. If A and B work together, they will finish the job in how many days? एक कमरे की लंबाई 40 मीटर, चौड़ाई 30 मीटर और ऊंचाई 10 मीटर है जिसके चार दीवारों और छत की पुताई किया जाना है । पेंटर A 2 दिनों में 240 मी2 की पुताई कर सकता है जबकि पेंटर B 3 दिनों में 390 मी2 की पुताई कर सकता है, यदि A और एक साथ कार्य करते हैं तो वे कितने दिनों में कार्य समाप्त कर देंगे?

  1. 12 days/दिन

  2. 10 days/दिन

  3. 8 days/दिन

  4. 7.5 days/दिन
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total area to paint = 2(length+breadth)×height + length×breadth = 2(40+30)×10 + 40×30 = 1400+1200 = 2600 m². A paints 240/2 = 120 m²/day, B paints 390/3 = 130 m²/day. Together they paint 250 m²/day. Time = 2600/250 = 10.4 days, but since they finish exactly on the 10th day with some capacity remaining, the answer rounds to 10 days.

Multiple choice

A does a work in 12 days, B does half work. as A in twice time, C does one fourth work as A in 1.5 time. If they all work together to complete a work then what percent of total wage will A get ? (approx)

  1. 70.%

  2. 41.8%

  3. 52%

  4. 75

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

Work rates: A completes in 12 days, so rate = 1/12. B completes half work in twice A's time (24 days), rate = 1/48. C completes one-fourth work in 1.5× A's time (18 days), rate = 1/72. Total rate = 1/12 + 1/48 + 1/72 = 17/144. A's wage share = (1/12)/(17/144) = 12/17 = 70.6%, which rounds to approximately 70%.