A Question on Rate

Construction of a building is planned to be completed in 22 days if done by 20 persons. After 10 days’ work, it is terminated for five days. In order for the building to be completed on time, (how many) additional workers are needed?

A) 40
B) 30
C) 25
D) 20

Solution:

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Answer: (A) 40 workers

Further Comments to enhance understanding:

(i) The phrase “additional workers” is a little ambiguous but by usage here, it is to be understood to mean “all 40 workers” the second time around need not necessarily be the same as the first badge of “20 workers” since the project was briefly “terminated”

(ii) Another trick is to note that completing the project on time means “within 7 days” and not necessarily 7 days

(iii) So, by trying T = 1, 2, 3,… 6,7 we see that only value of number of workers (which is both an integer & listed among the given choices A to D) is “40”. Hence, Answer = A) 40

(iv) For example, we reject the value t = 7 days possibility since the number of workers for this computation leads to 240/7 which is “not an integer” (hence impossible, so “reject”)