If 17 labourers can dig a ditch 26 m long in 18 days, working 8 hours a day; how many more labourers should be engaged to dig a similar ditch 39 m long in 6 days, each labourer working 9 hours a day ?

Answer: Option B

Let the total number of men to be engaged be $$x$$
More length, More labourers (Direct proportion)
Less days, More labourers (Indirect proportion)
$$\begin{array}{c}\text{Lentgh 26}:39\text{hfill}\\ \text{Days 6}:18\text{hfill}\\ \text{Hours per day }9:8\text{hfill}\end{array}\}::17:x$$
$$\begin{array}{rl}& \therefore 26\times 6\times 9\times x=39\times 18\times 8\times 17\\ & \iff x=\frac{\left(39\times 18\times 8\times 17\right)}{\left(26\times 6\times 9\right)}\\ & \iff x=68\end{array}$$
∴ Number of more labourers = (68 -17) = 51