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

2 employees and 3 trainees together can finish a project in 7 days, 6 employees and 13 trainees together can finish the same project in 2 days. Find the time taken by 4 employees and 4 trainees together to finish the same work.

  1. 5

  2. 6

  3. 4

  4. 3

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

Let e be one employee's daily work and t be one trainee's daily work. From first condition: 2e + 3t = 1/7. From second condition: 6e + 13t = 1/2. Subtracting 3×(first equation) from second: 4t = 1/2 - 3/7 = 1/14, so t = 1/56. Then 2e = 1/7 - 3/56 = 5/56, so e = 5/112. For 4 employees and 4 trainees: daily work = 4×(5/112) + 4×(1/56) = 20/112 + 4/56 = 20/112 + 8/112 = 28/112 = 1/4. Therefore 4 days needed.

Multiple choice

A and B can do a piece of work in 6 days and 8 days , respectively. With the help of C they can complete the work in 3 days and earned ₹1848. What was the share of C?

  1. ₹ 924

  2. ₹462

  3. ₹693

  4. ₹231
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Work rates: A = 1/6 per day, B = 1/8 per day. Combined A+B+C = 1/3 per day. So C's rate = 1/3 - 1/6 - 1/8 = 1/24 per day. Wages are distributed in ratio of work rates. C's share = (1/24)/(1/3) × 1848 = (1/8) × 1848 = ₹231. Option D is correct.

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?

  1. 24 days

  2. 36 days

  3. 18 days

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

A and B together take 6 days, so their combined rate is 1/6 work per day. A works 2 days and completes 25% (1/4) of the job, so A's rate is (1/4)÷2 = 1/8 work per day. B's rate = 1/6 - 1/8 = 1/24 work per day. Remaining work = 3/4. Time for B = (3/4)÷(1/24) = 18 days.

Multiple choice

N and T can complete typing of 2000 letters in 18 days and N works at a half of speed of the speed of T. If T leaves N 12 days after they both started working, then how many days delay will take place in completing this work?

  1. 12 days

  2. 6 days

  3. 18 days

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

N's speed is half of T's speed. Let T's rate = 2x letters/day, N's rate = x letters/day. Combined rate = 3x letters/day. Together for 12 days: 36x letters completed. Remaining: 2000 - 36x letters. N works alone at rate x: time = (2000 - 36x)/x = 2000/x - 36 days. Total time = 12 + 2000/x - 36 = 2000/x - 24 days. Normal time at combined rate: 2000/(3x) days. Delay = (2000/x - 24) - (2000/(3x)) = (4000/(3x) - 24). From 18 days together at rate 3x: 54x = 2000, x = 1000/27. Delay = 4000/(3×1000/27) - 24 = 36 - 24 = 12 days.

Multiple choice

P is four times as efficient as Q. P can complete a work in 45 days less than Q. If both of them work together, then in how many days the work will be completed?

  1. 10

  2. 12

  3. 15

  4. 30
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Since P is 4 times as efficient as Q, P takes 1/4 the time Q takes. Let Q take x days, then P takes x/4 days. Given P takes 45 days less: x - x/4 = 45, so 3x/4 = 45, x = 60. Q takes 60 days, P takes 15 days. Combined rate: 1/60 + 1/15 = 1/60 + 4/60 = 5/60 = 1/12. Together they complete the work in 12 days.

Multiple choice

A can do a work in 20 days, while B can do the same work in 25 days. They started the work jointly. Few days later C also joined them and thus all of them completed the whole work in 10 days. All of them were paid total of Rs.700. What is the share of C?

  1. 55

  2. 65

  3. 75

  4. 70
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A's rate is 1/20, B's rate is 1/25, and they work together for x days before C joins. C works for (10-x) days. The equation is x(1/20+1/25)+(10-x)(1/20+1/25+1/C)=1. Also x(1/20+1/25)=0.45 (work done before C joined). Solving gives x=5 and C's share proportion to 0.5/10 = 0.05. C's share = 0.05/0.1 * 700 = Rs. 70.

Multiple choice

Arun can complete a work in 10 days, Rahul can complete the same work in 20 days and Deepak in 40 days. Arun starts working on the first day, Rahul works for the second day and Deepak works for the third day. Again Arun works for fourth day and Rahul for fifth day and so on. If they continued working in the same way, in how many days will the work be completed?

  1. 15 days

  2. 16.5 days

  3. 15.5 days

  4. 17 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Work pattern repeats every 3 days: Day1(Arun)=1/10, Day2(Rahul)=1/20, Day3(Deepak)=1/40. Combined 3-day work = 1/10+1/20+1/40 = 4/40+2/40+1/40=7/40. After 15 days (5 cycles): 35/40 done. Day16 (Arun): 35/40+1/10=39/40. Day16.5 (Rahul half day): 39/40+1/40=40/40=1 complete.

Multiple choice

S and V can do a work in 12 days. M and S can do the same work in 16 days. M and V can do the same work in 24 days. In how many days S, V and M together can complete the same work?

  1. 32/3

  2. 10

  3. 16/3

  4. 11
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let S, V, M be the rates of work per day. S+V = 1/12, M+S = 1/16, M+V = 1/24. Adding all three equations: 2(S+V+M) = 1/12 + 1/16 + 1/24 = (4+3+2)/48 = 9/48 = 3/16. Therefore S+V+M = 3/32. Time taken together = 32/3 days.

Multiple choice

Ram can complete a piece of work in 15 days. He worked for 5 days and left. Mohan alone completed the remaining work in 20 days. How long would Mohan take to complete the whole work?

  1. 25

  2. 22

  3. 28

  4. 30

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

Ram's work rate: 1/15 per day. In 5 days, he completes 5 × (1/15) = 1/3 of the work. Remaining work = 2/3. Mohan completes 2/3 work in 20 days, so his rate is (2/3)/20 = 1/30 per day. Therefore, Mohan alone would take 30 days.

Multiple choice

A, B and C can do a work in 36, 72 and 54 days respectively. They started the work together but A left 8 days before the completion of the work and C left 12 days before the completion of the work. In how many days was the work completed?

  1. 21

  2. 20

  3. 24

  4. 25

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

Let total work = LCM(36, 72, 54) = 216 units. A's rate = 6/day, B's rate = 3/day, C's rate = 4/day. A worked for (d-8) days, C worked for (d-12) days, B worked for all d days. So 6(d-8) + 3d + 4(d-12) = 216. Solving: 6d - 48 + 3d + 4d - 48 = 216, so 13d = 312, giving d = 24 days.

Multiple choice

A and B can complete a work in 20 days whereas A and C can complete the same work in 30 days. C alone can complete the work in 40 days. A, B and C work together for 8 days. C alone will complete the remaining work in?

  1. 12 days

  2. 10 days

  3. 16 days

  4. 24 days

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

Let total work = 120 units (LCM of 20, 30, 40). A+B rate = 6/day, A+C rate = 4/day, C rate = 3/day. So A's rate = 3/day, B's rate = 3/day. All three together: 3+3+3 = 9/day. In 8 days, they complete 72 units. Remaining = 48 units. C alone at 3/day needs 16 days. The key is finding individual rates from combined rates.

Multiple choice

A can complete a certain work in 30 days. A started the work and B joined him after 4 days and the work was completed in total 20 days. In how many days can B alone complete the work?

  1. 42

  2. 45

  3. 48

  4. 50

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

A's work rate is 1/30 per day. In 4 days, A completes 4/30 work, leaving 26/30. A and B together complete the remaining 26/30 in 16 days, so (1/30 + 1/B) × 16 = 26/30. This gives 1/B = (26/30 - 16/30) / 16 = 10/480 = 1/48. Therefore B alone takes 48 days.

Multiple choice

P can complete a work in 21 days while Q is 25% less efficient than P. Q worked for 7 days and left , remaining work is completed by R in 27 days. Find in how many days R can complete the whole work alone ?

  1. 27 days

  2. 36 days

  3. 32 days

  4. 40 days

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

P's efficiency = 1/21 work per day. Q is 25% less efficient, so Q's efficiency = 0.75 × 1/21 = 3/84 = 1/28. Q worked for 7 days: 7/28 = 1/4 work done. Remaining work = 3/4, completed by R in 27 days. R's rate = (3/4)/27 = 1/36. So R alone takes 36 days.