Discussion Forum

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 ?

Answer:

Explanation:

Remaining work $=1-\frac{4}{7}$ $=\frac{3}{7}$

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)

$\left\{\begin{array}{c}Wrok\quad\quad\quad \frac{4}{7}:\frac{3}{7}\\ Days\quad\quad\quad 13:33\\Hrs/Day\quad\quad9:8\end{array}\right\}::117:x$  

$\frac{4}{7}\times 13\times 9\times x$ $=\frac{3}{7}\times 33\times 8\times 117$

or $x=\left(\frac{3\times 33\times 8\times 117}{4\times 13\times 9}\right)$  $=198 $

Additional men to be employed $=(198-117)$ = 81.