A contract is to be complete in 46 days and 117 men were set to work, each working 8 hours a day. After 33 days, 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: Option B

Remaining work
= $$\left(1-\frac{4}{7}\right)\text{ = }\frac{3}{7}$$
Remaining period = (46 - 33) = 13 days
Let the total men working at it be x
Less work, Less men (Direct proportion)
Less days, More men (Indirect proportion)
More hour/day, Less men (Indirect proportion)
$$\begin{array}{c}\text{Work }\frac{4}{7}:\frac{3}{7}\text{hfill}\\ \text{Men 13}:33\text{hfill}\\ \text{Hour/day }9:8\text{hfill}\end{array}\}::117:x$$
$$\begin{array}{rl}& \therefore \frac{4}{7}\times 13\times 9\times x=\frac{3}{7}\times 33\times 8\times 117\\ & \iff x=\frac{\left(3\times 33\times 8\times 117\right)}{\left(4\times 13\times 9\right)}\\ & \iff x=198\end{array}$$
∴ Addition men to be employed = (198 - 117) = 81