Question

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 1

Answer: (B)

81

Answer 2

The correct option is (B); Formula = $\frac{ M_{1} D_{1}H_{1}}{ W_{1} }$=$\frac{ M_{2} D_{2}H_{2}}{ W_{2} }$
117 men completed $\frac{4}{7}$ work in 33 days working 8 hours per day.
Let $x$ men complete the remaining $\frac{3}{7}$ work in 13 days working 9 hours per day.
$\frac{177\times33\times8}{4}$=$\frac{x\times13\times9}{3}$
$x = 33\times2\times3$ = 198
$\therefore$ Additional mens are 198-117 = 81