Question

A man wants to reach a certain destination. One-sixth of the total distance is muddy while half the distance is tar road. For the remaining distance he takes a boat. His speed of travelling in mud, in water, on tar road is in the ratio $3: 1: 5$. The ratio of the durations he requires to cross the patch of mud, stream and tar road is

• A. $\frac{1}{2}: \frac{4}{3}: \frac{5}{2}$
• B. $3: 8: 15$
• C. $10: 15: 18$
• D. $1: 2: 3$

Answer 1

Answer: (C)

Let the total distance $=x$
Muddy distance $=\frac{x}{6}$
Water distance $=\frac{x}{2}-\frac{x}{6}=\frac{x}{3}$
Tar distance $=\frac{x}{2}$
Speed travelling in mud $=3 y$
Speed travelling by stream $=4 y$
Speed travelling in tar $=5 y$
Ratio of time $=\frac{x / 6}{3 y}: \frac{x / 3}{4 y}: \frac{x / 2}{5 y}$
$=\frac{1}{18}: \frac{1}{12}: \frac{1}{10} $
$=\frac{10}{180}: \frac{15}{180}: \frac{18}{180} $
$=10: 15: 18$