Question

A man rows a boat a certain distance upstream and then returns to the same place. If the time taken by him in going upstream is twice the time taken in rowing downstream, find the ratio of the speed of the boat in still water and the speed of the stream.

• A. 2 : 1
• B. 3 : 2
• C. 5 : 3
• D. 3 : 1

Answer 1

The correct option is D 3 : 1

Since distance is constant for upstream and downstream.
So, time ratio = TU : TD = 2 : 1
$\therefore$ SU : SD = 1 : 2
$\therefore$ Speed of the boat in still water = $\frac{2+1}{2}=\frac{3}{2}$ km/h
And speed of the stream = $\frac{2-1}{2}=\frac{1}{2}$ km/h
$\therefore$ Required ratio = $\frac{\frac{3}{2}}{\frac{1}{2}}=\frac{3}{1}$ km/h

Alternate Approach:
Let speed of boat = x km/h
Speed of stream = y km/h
Upstream speed = (x - y) km/h
Downstream speed = (x + y) km/h
Since $\frac{D}{x-y}=\frac{2D}{x+y}\frac{x+y}{x-y}=\frac{2}{1}x/y=3:1.$