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 $=3y$
Speed travelling by stream $=4y$
Speed travelling in tar $=5y$
Ratio of time $=\frac{x/6}{3y}:\frac{x/3}{4y}:\frac{x/2}{5y}$
$=\frac{1}{18}:\frac{1}{12}:\frac{1}{10}$
$=\frac{10}{180}:\frac{15}{180}:\frac{18}{180}$
$=10:15:18$