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

Directions: Rahul works 2 days on 1st site and 5 days at 2nd site and gets Rs. 5400 and Rohit works 4 days on 1st site and 9 days at 2nd site and gets Rs. 9900. What is the wage of each day of 1st site?

  1. Rs. 900

  2. Rs. 450

  3. Rs. 1200

  4. Rs. 500
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let x be the wage for site 1 and y for site 2. 2x + 5y = 5400 and 4x + 9y = 9900. Multiplying the first by 2 gives 4x + 10y = 10800. Subtracting the second equation gives y = 900. Substituting back, 2x + 4500 = 5400, so 2x = 900, x = 450.

Multiple choice

Directions: Rahul works 2 days on 1st site and 5 days at 2nd site and gets Rs. 5400 and Rohit works 4 days on 1st site and 9 days at 2nd site and gets Rs. 9900. If Akash works for 4 days on 1st site and 3 days on 2nd site, what is his total wages?

  1. Rs. 4500

  2. Rs. 6000

  3. Rs. 7500

  4. Rs. 3600
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let x be the wage per day at site 1 and y be the wage per day at site 2. 2x + 5y = 5400 and 4x + 9y = 9900. Multiplying the first by 2 gives 4x + 10y = 10800. Subtracting the second from this gives y = 900. Then 2x + 5(900) = 5400, so 2x = 900, x = 450. Akash's wages: 4(450) + 3(900) = 1800 + 2700 = 4500.

Multiple choice

Mr. Grayson wanted to have a boundary wall around his garden. He hired three laborers of the same efficiency. The three worked together for 30 days, but during their work, they all did not come for a few days as they had to attend festive occasions. One of them did not come for 10 days more than the second laborer, and the third laborer did one-third of the total work. How many more days did the first laborer not come compared to the third laborer?

  1. 8

  2. 7

  3. 6

  4. 5

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

Elliot and Ellis started working at a computer company where they made computer parts. It took Elliot 70 days and Ellis 60 days to make a computer that was ready to sell. They began making the computer together, but Elliot left the work after some days due to illness, and it took Ellis 47 days to finish the remaining work alone. After how many days did Elliot leave?

  1. 5 days

  2. 7 days

  3. 8 days

  4. 9 days

  5. 11 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let x be the days they worked together. (x/70 + x/60) + 47/60 = 1. (x/70 + x/60) = 13/60. x * (6+7)/420 = 13/60. x * 13/420 = 13/60. x = 420/60 = 7.

Multiple choice

20 men are supposed to complete a work in 10 days. After working for 5 days, they realise that only one-fourth of the work is done. How many more men do they need to employ to finish the work on time?

  1. 40

  2. 30

  3. 20

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

Work done in 5 days by 20 men = 1/4. Remaining work = 3/4. Men required for 3/4 work in 5 days: (20 men * 5 days) / (1/4 work) = (M * 5 days) / (3/4 work). 20 * 5 * 4 = M * 5 * (4/3) -> M = 60. Additional men needed = 60 - 20 = 40.

Multiple choice

X is 60% more efficient than Y. They work together and complete a certain job. If X can complete the same job alone in 23 days, then on which day from the start of the work will they finish the job, working together?

  1. 11th day

  2. 13th day

  3. 15th day

  4. 18th day

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

X is 60% more efficient than Y, so X/Y = 160/100 = 8/5. If X takes 23 days, the total work is 8 * 23 = 184 units. Y's efficiency is 5 units/day. Together, they do 13 units/day. 184/13 is approximately 14.15, meaning they finish on the 15th day.

Multiple choice

Certain amount of work is completed by 10 men in 60 days working 9 hours a day. How many additional men will be required if the same work is to be completed in 30 days working 5 hours a day?

  1. 26

  2. 20

  3. 12

  4. 15

  5. 14
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the formula (M1 * D1 * H1) = (M2 * D2 * H2), we have (10 * 60 * 9) = (M2 * 30 * 5). Solving for M2 gives 5400 / 150 = 36 men. Since 10 men were already working, the additional men required is 36 - 10 = 26.

Multiple choice

Directions : Select the correct alternative from the given choices. lf A is 25% as efficient as B and can complete a certain work taking 15 days more than the time taken by B, in how many days will both A and B together complete the work?

  1. 4 days

  2. 5 days

  3. 7 days

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

If A is 25% as efficient as B, then B is 4 times as efficient as A. If A takes x days, B takes x/4 days. Given x = (x/4) + 15, we find 3x/4 = 15, so x = 20. A takes 20 days and B takes 5 days. Together, they take (20 * 5) / (20 + 5) = 100 / 25 = 4 days.

Multiple choice

Directions : Answer the question independently. A certain amount of work can be completed by 20 people in 100 days, working 12 hours a day. 5 people started the work, and starting from the second day, 7 people joined each day. Every alternate day, starting from the third day, two people left. If each person worked for two hours per day, then what fraction of the work was not completed after 60 days? (Assume efficiency of each person is the same)

  1. 7/80

  2. 5/80

  3. 1/20

  4. 3/40

  5. 5
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

Directions: Select the correct alternative from the given choices. If A starts a work, completes one-third of it and hands it over to B to complete the remaining work, it would take 40 days for the work be completed. Instead, if B first completes one-third of the work and then A takes over and completes the remaining work, it would take 35 days for the work to be completed. In how many day can A and B together complete the entire work?

  1. 16

  2. 24

  3. 18

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

Let A and B take x and y days to complete the work. (1/3)x + (2/3)y = 40 and (2/3)x + (1/3)y = 35. Multiply by 3: x + 2y = 120 and 2x + y = 105. Solving gives x=30, y=45. Together: 1/(1/30 + 1/45) = 1/(3/90 + 2/90) = 90/5 = 18 days.