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 certain number of men can complete a piece of work in 28 days. If there were 15 men more, the work could be finished in 10 days less. How many men are required to complete the work in reduced number of days?

  1. 42

  2. 23

  3. 32

  4. 27

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

Let M be the number of men. M * 28 = (M + 15) * (28 - 10). 28M = 18(M + 15). 28M = 18M + 270. 10M = 270. M = 27. The question asks for the number of men required to complete the work in the reduced time (18 days), which is M + 15 = 27 + 15 = 42.

Multiple choice

Ram, Suraj and Rajesh are working on a short duration project. Ram alone can complete the project in 8 days, Suraj can complete the project in 10 days, while Rajesh can do it in 12 days. They start the work together, but after 2 days Ram leaves the work and the remaining project is completed by Suraj and Rajesh. How long (approximately) will the project take to get completed?

  1. 4 days

  2. 3 days

  3. 2 days

  4. 2.5 days

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

Rates: Ram=1/8, Suraj=1/10, Rajesh=1/12. Combined rate = (15+12+10)/120 = 37/120. In 2 days, they do 2 * (37/120) = 37/60. Remaining work = 23/60. Suraj and Rajesh rate = 1/10 + 1/12 = 11/60. Time to finish = (23/60) / (11/60) = 23/11 = 2.09 days. Total time = 2 + 2.09 = 4.09 days, which is approximately 4 days.

Multiple choice

P and Q together can complete a work in 6 days. Q and R together can complete the same work in 15 days. P and R together can complete the work in 20/3 days. What is the ratio of number of days that Q alone takes to complete the work to the number of days that R alone takes to complete the work?

  1. 1:3

  2. 3:5

  3. 3:1

  4. 4:5

  5. 5:7
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let rates be P+Q=1/6, Q+R=1/15, P+R=3/20. Adding these gives 2(P+Q+R) = 1/6 + 1/15 + 3/20 = (10+4+9)/60 = 23/60, so P+Q+R = 23/120. R = (P+Q+R) - (P+Q) = 23/120 - 20/120 = 3/120 = 1/40 (40 days). Q = (P+Q+R) - (P+R) = 23/120 - 18/120 = 5/120 = 1/24 (24 days). Ratio Q:R = 24:40 = 3:5.

Multiple choice

Directions: The question given below is followed by three statements (A), (B) and (C). You have to determine which statement(s) is/are sufficient/necessary to answer the question. In how much time can 15 boys and 21 girls do the same work? A. 6 boys and 9 girls can do a piece of work in 12 days. B. One girl can complete the work in 468 days. C. 23 boys and 41 girls can do the same work in 3 days.

  1. Only statement A

  2. Only statement B

  3. Any two of them

  4. Either A or B

  5. All three statements
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let B be the work rate of a boy and G be the work rate of a girl. A: 6B + 9G = 1/12. B: G = 1/468. C: 23B + 41G = 1/3. With B and G, we have two variables. Any two equations are sufficient to solve for B and G, which then allows calculating the time for 15B + 21G.

Multiple choice

Directions: In this problem, a question is given followed by three statements numbered (I), (II) and (III). Read the statements carefully and determine which of them is/are sufficient/necessary to answer the question. In how many days will 4 men and 10 women finish the work? I. 3 men and 5 women can finish the work in 4 days. II. A man is 2.5 times efficient than a woman. III. 4 men can do the same work as 10 women can.

  1. Only statements I and II

  2. Only statements I and III

  3. Only statement I and either statement II or statement III

  4. All three statements

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

Statement I gives the rate of 3M+5W. Statement II gives M=2.5W. Statement III gives 4M=10W, which is equivalent to 2M=5W. Statement I and either II or III allow us to express the total work in terms of one variable (e.g., all women) and solve for the time taken by 4M+10W.

Multiple choice

20 young boys can do a particular work in 12 days, while the same can be completed by 15 experienced men in 10 days. What is the ratio of efficiency of a man to that of a young boy?

  1. 6 : 5

  2. 8 : 5

  3. 7 : 4

  4. 9 : 4

  5. 3 : 2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

20 boys * 12 days = 240 boy-days. 15 men * 10 days = 150 man-days. Since the work is the same, 150 men = 240 boys, so 1 man = 240/150 boys = 1.6 boys = 8/5 boys. The ratio of efficiency (man to boy) is 8:5.

Multiple choice

A is twice as efficient as B and B is twice as efficient as C. Time taken by C and D together to complete a piece of work is 4 days. If D takes 6 days to complete the same work alone, then how much time will A alone take to complete the same work?

  1. 3 days

  2. 2 days

  3. 4 days

  4. 5 days

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

Efficiency: A = 2B, B = 2C, so A = 4C. Let C's rate be c. A=4c, B=2c, C=c. C+D take 4 days, so c + d = 1/4. D takes 6 days, so d = 1/6. c = 1/4 - 1/6 = 3/12 - 2/12 = 1/12. A's rate = 4c = 4/12 = 1/3. A takes 3 days.

Multiple choice

Kyle, Megan and Chloe can complete a project in 5, 10 and 15 days, respectively. They started together to do the work. After 2 days, Kyle and Megan left. How many more days are needed by Chloe to complete the project?

  1. 8 days

  2. 6 days

  3. 5 days

  4. 4 days

  5. 4.5 days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Work rates: Kyle 1/5, Megan 1/10, Chloe 1/15. Together: 6/30 + 3/30 + 2/30 = 11/30 per day. In 2 days, they do 22/30. Remaining work is 8/30. Chloe takes (8/30) / (1/15) = 4 days.

Multiple choice

Chris and Robert build a house in 45 days and 40 days, respectively. They began building the house together, but Chris leaves after some days and then, Robert completes the remaining construction in 23 days. Chris left the construction after how many days?

  1. 6

  2. 8

  3. 9

  4. 12

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

Chris's rate = 1/45, Robert's rate = 1/40. Robert works alone for 23 days, completing 23/40 of the work. Remaining work = 1 - 23/40 = 17/40. They worked together for time T: T(1/45 + 1/40) = 17/40. T(8/360 + 9/360) = 17/40 => T(17/360) = 17/40 => T = 9 days.

Multiple choice

Jack alone can do a piece of work in 6 days and Jonny alone in 8 days. Jack and Jonny undertake to do it for Rs. 3200. With the help of Rehan, they completed the work in 3 days. How much is to be paid to Rehan?

  1. Rs. 385

  2. Rs. 400

  3. Rs. 550

  4. Rs. 785

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

Jack's efficiency is 1/6, Jonny's is 1/8. Together they do (1/6 + 1/8) = 7/24 per day. In 3 days, they do 3 * (7/24) = 7/8 of the work. Rehan does 1/8 of the work. Payment is proportional to work: (1/8) * 3200 = 400.

Multiple choice

Ronit, Alan and Paul can do a piece of work in 20, 30 and 60 days, respectively. In how many days can Ronit do the work, if he is assisted by Alan and Paul on every third day?

  1. 12 days

  2. 15 days

  3. 16 days

  4. 18 days

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

Ronit's rate is 1/20, Alan's is 1/30, and Paul's is 1/60. In a 3-day cycle, Ronit works alone for 2 days (2/20) and with others on the 3rd day (1/20 + 1/30 + 1/60 = 6/60 = 1/10). Total work in 3 days is 2/20 + 1/10 = 1/10 + 1/10 = 1/5. Thus, 5 cycles of 3 days (15 days) complete the work.