Question

Two boats P and Q travels downstream from A to B. The ratio of time taken to cover the distance from A to B by both boat is 4 : 5. If speed of boat Q is 34 km/h and speed of stream is 6 km/h, what will be the speed of  boat P, when it travel from B to A?
1. 40 km/h
2. 50 km/h
3. 44 km/h
4. 38 km/h
5. None of these

Answer 1

Correct Answer - Option 4 : 38 km/h

Given: 

The ratio of time taken to cover the distance from A to B by both boats is 4 : 5

The speed of boat Q is 34 km/h

Concept: 

When distance is constant 

The ratio of speed is equal to inverse the ratio of time.

Hence, if the ratio of the speed of A : B is 4 : 5, the ratio of time taken by A and B would be 5 : 4. 

Calculation: 

Let the speed of boat P be x km/h.

According to the question 

The speed of boat P downstream is (x + 6) km/h

The speed of boat Q in downstream is (34 + 6) = 40 km/h 

Now, 

The ratio of the speed of boat P and Q is 

⇒ (x + 6) : 40 = 5 : 4

⇒ x + 6 = 50

⇒ x = 44 km/h

So, 

The speed of boat P, when It travels from B to A (upstream)

⇒ 44 - 6 

⇒ 38 km/h

∴ 38 km/h