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

Akshar, Akshay and Akshat have to read a document of seventy eight pages and make a presentation next day. They realize that the article is difficult to understand and they would require team work to finish the assignment. Akshar can read a page in 2 min, Akshay in 3 min, and Akshat in 4 min. If they divide the article into 3 parts so that all three of them spend the equal amount of time on the article, the number of pages that Akshay should read is

  1. 24

  2. 36

  3. 25

  4. 35
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let T be the time each spends. Pages read by Akshar = T/2, Akshay = T/3, Akshat = T/4. Total pages = T/2 + T/3 + T/4 = 78. (6T + 4T + 3T)/12 = 78 => 13T/12 = 78 => T = 72. Akshay reads 72/3 = 24 pages.

Multiple choice

When working alone A, B and C can complete a piece of work in 8, 12 and 30 days respectively. At the most only two people can work on each day and nobody works for more than two consecutive days. What is the minimum number of days that they will take to finish the work?

  1. 5 4/25

  2. 6 4/21

  3. 6 4/25

  4. 7 4/25
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The total work is 120 units (LCM of 8, 12, 30). A, B, and C do 15, 10, and 4 units per day respectively. To minimize days, we maximize work per day using the two most efficient workers (A and B) for two days, then rotate to keep the constraint of no more than two consecutive days for anyone.

Multiple choice

P is thrice as good a workman as Q and therefore became able to finish a job in 48 days less than Q. Working together, they can do it in how many days?

  1. 18

  2. 16

  3. 15

  4. 12
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Since P is thrice as efficient as Q, the ratio of time taken by P and Q is 1 : 3. The difference in their time is 2 parts, which corresponds to 48 days, meaning P takes 24 days and Q takes 72 days. Working together, they will complete the job in (24 * 72) / (24 + 72) = 18 days.

Multiple choice

A can do a piece of work in 12 days alone, B can do the same work in 16 days alone. After A has been working for 5 days and B for 7 days, C finishes it in 14 days. In how many days will C alone be able to do the work?

  1. 96

  2. 86

  3. 90

  4. 80
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A's rate = 1/12, B's = 1/16. A works 5 days: 5/12. B works 7 days: 7/16. Total work done = 5/12 + 7/16 = (20+21)/48 = 41/48. Remaining work = 7/48. C finishes in 14 days, so C's rate = (7/48) / 14 = 1/96. C alone takes 96 days.

Multiple choice

The cost of digging a pit was Rs 1,347. How much will it cost (approximately)if the wages of workmen per day has been increased by 1/8 of their former wage and working time decreased by 1/21 of the former time? (Note:- except above information other things remain unchanged )

  1. 1401

  2. 1421

  3. 1443

  4. 1479
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

New cost = Old cost * (1 + 1/8) * (1 - 1/21) = 1347 * (9/8) * (20/21) = 1347 * (180/168) = 1347 * (15/14) = 1443.21.

Multiple choice

To complete a certain piece of work, the time taken by A and C is 2 days more than that taken by A, B and C. The time taken by B and C is 150% more than that taken by A, B and C to complete the work. A, B and C together completed the work earning a total of Rs.9860 in which the share of C is Rs.1479. How many days did A, B, C take to complete the work?

  1. 5 1/3

  2. 7 1/2

  3. 5

  4. 6
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let T be the time taken by A, B, C. A+C = T+2, B+C = 2.5T. Using work rates: 1/(T+2) + 1/(2.5T) - 1/T = 1/C. Also, C's share of earnings is proportional to his work rate. Solving these equations yields T = 6.

Multiple choice

K and L can do a work in 15 and 20 days, respectively. They work together for 5 days and leave. Calculate the unfinished portion of the work. k এবং L যথাক্রমে 15 এবং 20 দিনের মধ্যে একটি কাজ করতে পারেন। তারা একসাথে 5 দিন কাজ করে চলে যায়। কাজের অসম্পূর্ণ অংশ ?

  1. 7/12

  2. 5/12

  3. 1/13

  4. 1/4
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

K's rate = 1/15, L's rate = 1/20. Combined rate = 1/15 + 1/20 = 7/60. Work done in 5 days = 5 * (7/60) = 35/60 = 7/12. Unfinished work = 1 - 7/12 = 5/12.

Multiple choice

Directions: The following question consists of three statements I, II and III. You have to determine which of the following statements is/are necessary to answer the question. 15 men and 6 women can complete a job in 4 days. How many days will it take for 10 men and 4 children to complete the same job? I. 5 men can complete the work in 15 days. II. 1 child takes double the time taken by a woman to complete the same job. III. 3 women can complete this job in 40 days

  1. II and either I or III

  2. Only II or III

  3. Only III

  4. Any two of the three

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

To solve for 10 men and 4 children, we need the work rates of men, women, and children. Statement I gives the rate of men. Statement III gives the rate of women. Statement II relates children to women. We need to know the relationship between men and women to combine these, or have enough info to solve the system. II and either I or III are sufficient to establish the ratios.