Question : (N + 15) persons working 9 hours a day can complete 36% of a work in 8 days. (N + 9) persons can complete the remaining work in 20 days if each of them works for 7 hours per day. Determine the value of N.
Option 1: 55
Option 2: 52
Option 3: 64
Option 4: 50
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Correct Answer: 55
Solution :
Let the total work as W.
The work done is proportional to the number of persons, the number of hours worked per day, and the number of days.
We have (N + 15) persons, each working for 9 hours a day, who can complete 36% of the work in 8 days.
⇒ (N + 15) × 9 × 8 = 0.36 × W
⇒ 72(N + 15) = 0.36 × W .............................(i)
We have (N + 9) persons who can complete the remaining work in 20 days if each works for 7 hours daily.
⇒ (N + 9) × 7 × 20 = 0.64 × W
⇒ 140(N + 9) = 0.64 W ............................(ii)
Solving equations (i) and (ii), we get
N = 55 and W = 14000
Hence, the correct answer is 55.
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