A contract is to be completed in 46 days and 117 men were set to work, each working 8 hours a day. After 33 days, $\frac{4}{7}$ of the work is completed. How many additional men may be employed so that the work may be completed in time, each man now working 9 hours a day?
(a)80
(b)81
(c)82
(d)83
Answer
Answer (as printed): B
Explanation
Remaining work $= \left(1-\frac{4}{7}\right) = \frac{3}{7}$. Remaining period $= (46-33)$ days $= 13$ days. Let the total men working at it be $x$. Less work, Less men (Direct Proportion). Less days, More men (Indirect Proportion). More Hrs/Day, Less men (Indirect Proportion). Work $\frac{4}{7}:\frac{3}{7}$, Days $13:33$, Hrs/Day $9:8$ :: $117:x$. $\therefore \frac{4}{7} \times 13 \times 9 \times x = \frac{3}{7} \times 33 \times 8 \times 117 \Leftrightarrow x = \frac{3 \times 33 \times 8 \times 117}{4 \times 13 \times 9} = 198$. $\therefore$ Additional men to be employed $= (198-117) = 81$.
Explanation as extracted from the printed page; notation may be imperfect.