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

Adolf can do a task in 15 days, but Beggie can do the same task in 25 days. Both started working together, but after 6 days, Adolf left. In how many days will Beggie complete the remaining task?

  1. 27

  2. 9

  3. 17

  4. 25

  5. 26
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Adolf's rate is 1/15, Beggie's is 1/25. In 6 days, they do 6(1/15 + 1/25) = 6(5/75 + 3/75) = 6(8/75) = 48/75 = 16/25 of the work. Remaining work is 9/25. Beggie finishes this in (9/25) / (1/25) = 9 days.

Multiple choice

Each of Selena, Rajavi and Priya needs a unique time to complete a piece of work. Selena takes 6 days less than the time taken by Rajavi to finish the same work. Both Selena and Rajavi together can finish it in 4 days and Priya takes 2 days more than the time taken by Selena to complete the same work. How many days will Rajavi take to complete the work?

  1. 8 days

  2. 10 days

  3. 13 days

  4. 12 days

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

Let Rajavi take R days. Selena takes R-6 days. Together: 1/R + 1/(R-6) = 1/4. Solving: (R-6+R)/(R(R-6)) = 1/4, so 4(2R-6) = R^2-6R, 8R-24 = R^2-6R, R^2-14R+24 = 0. (R-12)(R-2) = 0. Since R must be greater than 6, R = 12.

Multiple choice

The content development team of an educational company was working at a uniform rate to develop 2000 questions in 10 days. But after working for 6 days, the content development team was informed by the company management team that the remaining questions had to be developed in 1 day. By what percentage does the content team need to increase its rate of development of questions, so that it can complete development of the remaining questions in 1 day?

  1. 300%

  2. 400%

  3. 500%

  4. 250%

  5. 600%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Initial rate = 2000/10 = 200 questions/day. After 6 days, 1200 questions are done, leaving 800. To finish 800 in 1 day, the new rate must be 800 questions/day. The increase is (800 - 200) / 200 = 600 / 200 = 300%.

Multiple choice

Ram and Sandhu took a contract to do a work together for Rs. 600. Ram alone is able to complete it in 16 days and Sandhu alone is able to complete it in 24 days. If Sunita helps them, they can finish the work in 8 days only. How much money will Ram get when Sunita helps?

  1. Rs. 200

  2. Rs. 300

  3. Rs. 100

  4. Rs. 400

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

Work rates: Ram = 1/16, Sandhu = 1/24. Together = 1/16 + 1/24 = 5/48. With Sunita, rate = 1/8. Sunita's rate = 1/8 - 5/48 = 1/48. Total work is shared in ratio of rates: 1/16 : 1/24 : 1/48 = 6 : 4 : 2 = 3 : 2 : 1. Ram's share = (3/6) * 600 = 300.

Multiple choice

A can do a certain job in 25 days which B alone can do in 20 days. A started the work and was joined by B after 10 days. The work lasted for

  1. 25/2 days

  2. 128/9 days

  3. 15 days

  4. 50/3 days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A's rate = 1/25, B's rate = 1/20. In 10 days, A completes 10/25 = 2/5 of the work. Remaining work = 3/5. Combined rate = 1/25 + 1/20 = 9/100. Time for remaining work = (3/5) / (9/100) = (3/5) * (100/9) = 20/3 days. Total time = 10 + 20/3 = 50/3 days.

Multiple choice

6 men and 8 women can complete a job in 20 days, while 8 men and 22 women can complete it in 10 days. Find the time taken by 34 women to complete the same job.

  1. 10 days

  2. 12 days

  3. 15 days

  4. 18 days

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

Let M and W be the work done by one man and one woman per day. 20(6M + 8W) = 10(8M + 22W). 120M + 160W = 80M + 220W. 40M = 60W, so 2M = 3W. Total work = 20(6M + 8(2/3)M) = 20(6M + 16/3 M) = 20(34/3 M) = 680/3 M. Time for 34 women = (680/3 M) / (34 * 2/3 M) = 680 / 68 = 10 days.

Multiple choice

Women, men and children are employed to do a piece of work in the proportion 3 : 2 : 1 and their wages are in the proportion 5 : 3 : 2. When 90 women are employed, total daily wages of all amounts to Rs. 11,730. Find the daily wage of a woman.

  1. Rs. 65

  2. Rs. 85

  3. Rs. 80

  4. Rs. 60

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

Let the number of workers be 3x, 2x, x for women, men, children. Given 3x = 90, so x = 30. Total workers: 90 women, 60 men, 30 children. Let wages be 5y, 3y, 2y. Total wage = 90(5y) + 60(3y) + 30(2y) = 450y + 180y + 60y = 690y. 690y = 11730, so y = 17. A woman's daily wage is 5y = 5 * 17 = 85.

Multiple choice

Together X and Y can complete a piece of work in 9 days, Y and Z in 12 days and X and Z in 18 days. Who is the most efficient worker among X, Y and Z?

  1. X

  2. Y

  3. Z

  4. Cannot be determined
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let X, Y, Z be their rates. X+Y = 1/9, Y+Z = 1/12, X+Z = 1/18. Adding these: 2(X+Y+Z) = 1/9 + 1/12 + 1/18 = (4+3+2)/36 = 9/36 = 1/4. So X+Y+Z = 1/8. Then Z = 1/8 - 1/9 = 1/72; X = 1/8 - 1/12 = 1/24; Y = 1/8 - 1/18 = 5/72. Comparing 1/24, 5/72, 1/72, Y is the largest.