Question

The ratio of speed of boat in still water to the speed of stream is 5 : 2. It takes 4 hour more to travel 42 km upstream than to travel same distance downstream. Find the speed of boat in still water.

1. 12 km/hr
2. 10 km/hr
3. 15 km/hr
4. 20 km/hr
5. 17 km/hr

Answer 1

Correct Answer - Option 2 : 10 km/hr

Let the speed of boat in still water be u km/hr and the speed of the stream is v km/hr.

Given:                            

u : v = 5 : 2

Formula Used:

Speed while travelling downstream = u + v

Speed while travelling upstream = u - v           

Calculations:

Let u = 5x and v = 2x

Speed while travelling downstream = 5x + 2x = 7x

Speed while travelling upstream = u-v = 5x - 2x = 3x

Time(upstream) = 42/3x and  Time(downstream) = 42/7x

It is given that it takes 4 hour more to travel 42 km upstream than to travel same distance downstream.

⇒ 42/3x = 42/7x +4

⇒ 14/x = 6/x + 4

⇒ 8/x = 4

⇒ x = 2

Speed in still water = u = 5x

⇒ 5 × 2 = 10 km/hr