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

Athiya and Dean can do a piece of work in 30 days, while Dean and Cathy does the same work in 24 days. Athiya and Cathy can complete the same work in 20 days. They all work for 10 days and then, Dean and Cathy leave. How many more days will Athiya take to finish the work?

  1. 26 days

  2. 22 days

  3. 18 days

  4. 14 days

  5. 28 days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The combined daily work rate of Athiya, Dean, and Cathy is half of (1/30 + 1/24 + 1/20), which is 1/16. In 10 days, they complete 10/16 = 5/8 of the work, leaving 3/8 of the work remaining. Athiya's individual daily work rate is 1/16 - 1/24 = 1/48, meaning she would take 48 days to do the whole work alone; thus, she needs 48 * (3/8) = 18 more days to finish the remaining work.

Multiple choice

A can do a piece of work in 20 days and B can do the same piece of work in 30 days. They start working together and work for 5 days and then, both leave the work. C alone finishes the remaining work in 14 days. In how many days will C alone finish the whole work?

  1. 24

  2. 18

  3. 36

  4. 42
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A's rate = 1/20, B's rate = 1/30. Combined rate = 1/20 + 1/30 = 5/60 = 1/12. In 5 days, they do 5/12 of the work. Remaining work = 7/12. C does 7/12 in 14 days, so C's rate = (7/12) / 14 = 1/24. C takes 24 days to finish the whole work.

Multiple choice

X and Y can complete a piece of work in 12 and 60 days, respectively. They contracted to complete the work together for Rs. 24,000. What will be the share (in Rs.) of X?

  1. 18,000

  2. 16,000

  3. 20,000

  4. 21,000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The ratio of work done by X and Y is inversely proportional to the time taken. X takes 12 days and Y takes 60 days, so the ratio of their work is 60:12, which simplifies to 5:1. X's share is (5/6) * 24000 = 20000.

Multiple choice

Krishika and Jaya are making a flower pot at an exhibition for some charity work for Rs. 450. Krishika alone can make it in 4 days, while Jaya individually can make it in 6 days. If they take the help of Chahat, then they can make the pot in 2 days. What would be Chahat's share of the work done?

  1. 70

  2. 75

  3. 80

  4. 85

  5. 90
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Krishika rate = 1/4, Jaya rate = 1/6. Together (K+J+C) rate = 1/2. Chahat rate = 1/2 - (1/4 + 1/6) = 1/2 - 5/12 = 1/12. Chahat's share = (1/12) / (1/2) * 450 = (1/6) * 450 = 75.

Multiple choice

Thirty-eight equally efficient men can do a piece of work in 5 days. If, however, only one man comes to work on the 1st day and with each passing day, one man joins him, then in how many days will the work be completed?

  1. 18

  2. 16

  3. 17

  4. 19

  5. 20
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total work = 38 * 5 = 190 man-days. On day n, n men work. Total work after n days is the sum of the first n integers: n(n+1)/2. We need n(n+1)/2 >= 190, so n(n+1) >= 380. For n=19, 19*20/2 = 190.