If 17 labourers can dig a ditch 20 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?
(a)34
(b)51
(c)68
(d)85
Answer
Answer (as printed): B
Explanation
Let the total number of men to be engaged be $x$. More length, More labourers (Direct Proportion). Less days, More labourers (Indirect Proportion). More hours per day, Less labourers (Indirect Proportion). Length $26:39$, Days $6:18$, Hours per day $9:8$ :: $17:x$. $\therefore (26 \times 6 \times 9 \times x) = (39 \times 18 \times 8 \times 17) \Leftrightarrow x = \frac{(39 \times 18 \times 8 \times 17)}{(26 \times 6 \times 9)} = 68$. $\therefore$ Number of more labourers $= (68-17) = 51$.
Explanation as extracted from the printed page; notation may be imperfect.