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 ration $3:4:5$. The ratio of the duration 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

The correct option is C $10:15:18$

Let the total distance be $x$

Muddy distance $=\frac{x}{6}$

Speed in mud $=3v$

time in mud $=t_1=\frac{\frac{x}{6}}{3v}=\frac{x}{18v}$

Distance by tar road $=\frac{x}{2}$

speed on tar road $=5v$

time on tar road$=t_2=\frac{\frac{x}{2}}{5v}=\frac{x}{10v}$

Distance by water $=x-\frac{x}{2}-\frac{x}{6}=\frac{x}{3}$

speed in water$=4v$

time in water $=t_3=\frac{\frac{x}{3}}{4v}=\frac{x}{12v}$

$t_1:t_3:t_2=\frac{x}{18v}:\frac{x}{12v}:\frac{x}{10v}{t}_1:t_3:t_2=10:15:18$

So opton $C$ is correct