A certain number of persons can dig a trench 100 m long, 50 m broad and 10 m deep in 10 days. The same number of persons can dig another trench 20 m broad and 15 m deep in 30 days. The length of the second trench is
(a)400 m
(b)500 m
(c)800 m
(d)900 m
Answer
Answer (as printed): B
Explanation
Let the required length be $x$ metres. Less breadth, More length (Indirect Proportion). More depth, Less length (Indirect Proportion). More days, More length (Direct Proportion). Breadth $20:50$, Depth $15:10$, Days $10:30$ :: $100:x$. $\therefore 20 \times 15 \times 10 \times x = 50 \times 10 \times 30 \times 100 \Leftrightarrow x = \frac{(50 \times 10 \times 30 \times 100)}{(20 \times 15 \times 10)} \Leftrightarrow x = 500$.
Explanation as extracted from the printed page; notation may be imperfect.