Question

A motorboat whose speed in still water is 15 km/hr, goes 30 km downstream and comes back in 4 hrs and 30 minutes. The speed of the stream (in km/hr) is
1. 10
2. 6
3. 5
4. 4

Answer 1

Correct Answer - Option 3 : 5

Given:

Speed in still water = 15 km/hr

Downstream = 30 km 

Total time taken to comes back = 4 hrs 30 min

Formula used:

Time = Distance/Speed

Upstream = x – y

Downstream = x + y

Calculation:

Let the speed of the stream be x km/hr

speed downstream = (15 + x) km/hr

speed upstream = (15 – x) km/hr

Time upstream = Distance upstream/Speed upstream

⇒ 30/15 – x

Time downstream = Distance downstream/Speed downstream

⇒ 30/15 + x

According to question

⇒ 4.5 = 30/(15 – x) + 30/(15 + x)

⇒ 4.5 = 30(15 + x) + 30(15 – x)/225 – x²

⇒ 4.5 = 900/225 – x²

⇒ 225 – x² = 200

⇒ x² = 25

⇒ x = 5 km/hr

∴ The speed of the stream is 5