Question : (N + 18) persons, each working for 7.5 hours a day, can complete 48% of the work in 20 days. (N + 12) persons can complete the remaining work in 30 days if each works 6.5 hours per day. Determine the value of N.
Option 1: 18
Option 2: 16
Option 3: 20
Option 4: 22
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Correct Answer: 18
Solution : Number of hours (N + 18) people worked in a day, $T_1$ = 7.5 hours Number of days they worked for, $D_1$ = 20 days Fraction of work completed by them, $W_1$ = 0.48 Number of hours (N + 12) people worked in a day, $T_2$ = 6.5 hours Fraction of work completed by them, $W_2$ = 0.52 Number of days they worked for, $D_2$ = 30 days Now, we know $\frac{M_1\times D_1\times T_1}{W_1}=\frac{M_2\times D_2\times T_2}{W_2}$ So, $\frac{(N+18)\times 20\times 7.5}{0.48}=\frac{(N+12)\times 6.5\times 30}{0.52}$ ⇒ $(N+18) =(N+18)\times 12 $ ⇒ $11N=18\times 11$ ⇒ $N= 18$ Hence, the correct answer is 18.
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