Question

The time taken for a boat to travel from point P to Q to the time taken to travel from point Q to P is in the ratio 3 : 2. The total time taken is 5 hrs. How much time (in hours) will it take for the journey if the water was still?
1. 4.2 hours
2. 4.8 hours
3. 5 hours
4. 5.2 hours

Answer 1

Correct Answer - Option 2 : 4.8 hours

Given:

Ratio = P to Q : Q to P = 3 : 2

Total time is taken = 5 hours

Formula used:

Time = Distance/Speed

Calculation:

Let d be the distance between P and Q

And, Let speed of boat and speed of stream be u and v repectively.

According to the question

⇒ Upstram time : Downstream time = 3 ∶ 2

⇒ [d/(u - v)] : [d/(u + v)] = 3 ∶ 2

⇒ (u + v) : (u - v) = 3 ∶ 2

⇒ u = 5v

Total time = (d/(u - v)) + (d/(u + v)) 

⇒ (d/4v) + (d/6v)

⇒ 10d/24v 

⇒ d/v = 12

Time taken, if water was still = 2d/u

⇒ 2d/5v = (2/5) × 12

⇒ 4.8 hrs

∴ Required time is 4.8 hours.

A boat takes more time to cover the distance when its direction is against water = Upstream

A boat takes less time to cover the distance when its direction is along the stream = Downstream