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

Asha and Bhuvan can do a piece of work in 6 days and 9 days, respectively. They work on alternate days, starting with Asha on the first day. In how many days will the work be completed?

  1. 6 days

  2. 7 days

  3. 9 days

  4. 8 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Asha completes 1/6 of work per day, Bhuvan completes 1/9 per day. They work alternately starting with Asha. Day 1-6 (3 cycles): Asha does 3/6=1/2, Bhuvan does 3/9=1/3. Total after 6 days = 1/2+1/3=5/6. Remaining work = 1/6. Day 7 (Asha's turn): She needs 1 day for her 1/6 portion, but only 1/6 remains. So she completes it in 1/6 ÷ (1/6) = 1 day. Total = 7 days. Option B is correct. Option A(6 days) is too early, C(9 days) and D(8 days) are too late.

Multiple choice

Anshu, Swati and Rajni can finish a work in 4 days if they work together. However, Anshu alone will take 9 days to complete the work, and Swati alone will complete the work in 12 days. How many days will Rajni alone take to complete the work?

  1. 18

  2. 12

  3. 24

  4. 16
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In 1 day, Anshu completes 1/9 of the work, Swati completes 1/12, and together with Rajni they complete 1/4. Therefore, Rajni's daily work rate is 1/4 - 1/9 - 1/12 = 1/18, which means she alone would take 18 days to complete the work.

Multiple choice

5 men and 8 women can complete a task in 34 days, whereas 4 men and 18 women can complete the same task in 28 days. In how many days can the same task be completed by 3 men and 5 women?

  1. 72

  2. 56

  3. 64

  4. 36
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let m be man's 1-day work and w be woman's 1-day work. From given: 5m + 8w = 1/34 and 4m + 18w = 1/28. Solving: m = 2/170, w = 3/170. For 3 men and 5 women: 3m + 5w = 3(2/170) + 5(3/170) = 21/170. Days needed: 170/21 ≈ 8, so 170/21 × 7 = 56 days. Option B is correct.

Multiple choice

P can do (2/5)th part of a work in 12 days, while Q can do (3/4)th of the same work in 15 days. In how many days both will complete the work if they worked together? P किसी काम का (2/5) भाग 12 दिन में समाप्त कर सकता है, जबकि Q इसी काम का (3/4) भाग 15 दिन में कर सकता है | दोनों मिलकर इस काम को कितने दिन में समाप्त कर सकेंगें?

  1. 10 days 10 दिन

  2. 12 days 12 दिन

  3. 15 days 15 दिन

  4. 18 days 18 दिन

  5. 24 days 24 दिन
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

P does 2/5 work in 12 days, so P's full work time = 12 × 5/2 = 30 days. Q does 3/4 work in 15 days, so Q's full work time = 15 × 4/3 = 20 days. Together in 1 day: 1/30 + 1/20 = 5/60 = 1/12, so they complete the work in 12 days.

Multiple choice

12 women can complete a work in 52 days, then find how many women will be required to complete (2/3)rd of the same work in 13 days? 12 महिलाएं एक कार्य को 52 दिनों में पूरा कर सकती हैं, तो ज्ञात कीजिए कि उसी कार्य का (2/3) भाग 13 दिनों में पूरा करने के लिए कितनी महिलाओं की आवश्यकता होगी?

  1. 32

  2. 30

  3. 26

  4. 28

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

Total work = 12 women × 52 days = 624 woman-days. (2/3) of work = 624 × (2/3) = 416 woman-days. Women needed = 416 ÷ 13 = 32 women. Use inverse proportion: more work in less time requires more workers.

Multiple choice

The ratio of work efficiency of P and Q is 2:3 and that of Q and R is 4:5. If P can complete project in 30 days and all three are paid Rs.700 per day for the total work done in the same ratio as their work efficiency, what salary would be earned by R for the total number of days he worked on the project?

  1. Rs. 5000

  2. Rs. 3000

  3. Rs. 4500

  4. Rs. 4800
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

P:Q efficiency = 2:3, Q:R = 4:5. Combined P:Q:R = 8:12:15. P completes project in 30 days, so P's efficiency = 1/30. Let total work = 1. P's share = 8/35 of work. Payment is Rs.700/day per efficiency unit. R's efficiency = 15/8 × P = 15/8 × 1/30 = 1/16. R works for 16 days earning 16×700×(15/35) = Rs.4800.

Multiple choice

16 workers working 6 hours a day can build a wall of length 150 meters, breadth 20 meters, and height 12 meters in 25 days. In how many days 12 workers, working 8 hours a day can build a wall of 800 meters length, 15 meters breadth, and 6 meters height?

  1. 80 days

  2. 70 days

  3. 50 days

  4. 45 days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume1 = 150×20×12 = 36000. Volume2 = 800×15×6 = 72000 (double). Worker-hours1 = 16×6×25 = 2400. Worker-hours2 = 12×8×d. Using chain rule: 36000/2400 = 72000/(96d). Solving gives d = 50.

Multiple choice

If 30 persons take 10 days to complete a certain work working 8 hours a day, then 40 persons should work how many hours a day so that the work is completed in 6 days?

  1. 12

  2. 8

  3. 6

  4. 10
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total work = 30 persons × 10 days × 8 hours/day = 2400 person-hours. This same work must be completed by 40 persons in 6 days. Let h be hours per day. Then 40 × 6 × h = 2400, so 240h = 2400, giving h = 10 hours per day. This is an inverse variation problem - more people means fewer hours needed.

Multiple choice

A can do 2/5 of a work in 6 days and B can do 2/3 of the same work in 12 days. A and B worked together for 6 days. C alone completed the remaining work in 8 days. A and C, working together, will complete the same work in:

  1. 12 days

  2. 9 days

  3. 10 days

  4. 8 days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A does 2/5 work in 6 days, so rate = 1/15 per day. B does 2/3 work in 12 days, so rate = 1/18 per day. Together they do 11/90 per day. In 6 days: 44/90 done, 46/90 left. C does 46/90 in 8 days, so C's rate = 23/360 per day. A + C together: 1/15 + 23/360 = 47/360 per day, so time = 360/47 ≈ 7.66 days, which rounds to 8 days. The answer is correct.

Multiple choice

Ratio between efficiency of A, B and R is 6 : 4 : 5. All three starts to work together with same efficiency. But R, destroys his 60% of work in every evening, due to which they have to work 20 more days than estimated time. Find the estimated days by them to complete the work.

  1. 80

  2. 45

  3. 36

  4. 49

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

Let total work = 1 unit, combined efficiency = 6+4+5=15 units/day. Estimated days = 1/15. With R's 60% evening destruction, net daily work = 15 - 60% of 5 = 12 units. Actual days = 1/12. Given actual = estimated + 20 days: 1/12 - 1/15 = 20. Solving: (5-4)/60 = 20, so 1/60 = 20, giving estimated days = 80. The key is recognizing that 20 extra days come from reduced net efficiency.