A contract is to be completed in 50 days and 105 men were set to work, each working 8 hours a day. After 25 days, $\frac{2}{5}$ of the work is finished. How many additional men be employed so that the work may be completed on time, each man now working 9 hours a day? (SNAP., 2010)
Answer
Answer (as printed):
Explanation
Let the required number of additional men be $x$. Remaining work $=\left(1-\frac{2}{5}\right)=\frac{3}{5}$. More days, less men (Indirect Proportion). More working hours per day, Less men (Indirect Proportion). More work, More men (Direct Proportion). Days $25:25$, Working hours $9:8$, Work $\frac{2}{5}:\frac{3}{5}$ :: $105:(105+x)$. $\therefore 25 \times 9 \times \frac{2}{5} \times (105+x) = 25 \times 8 \times \frac{3}{5} \times 105 \Leftrightarrow (105+x) = 8 \times \frac{3}{5} \times 105 \times \frac{5}{2} \times \frac{1}{9} = 140 \Leftrightarrow x=35$. Hence, additional number of men required = 35.
Explanation as extracted from the printed page; notation may be imperfect.