Question

The speed of a boat in still water is 5 km/hr. If it takes thrice as much time in going 20 km upstream as in going the same distance downstream, find the speed of the stream.

• A. 2.5 km/hr
• B. 3.5 km/hr
• C. 4.5 km/hr
• D. 5.5 km/hr

Answer 1

The Correct Option is A

To solve the problem, we need to find the speed of the stream given that the speed of the boat in still water is 5 km/hr. The problem states that it takes thrice as much time to travel 20 km upstream as it does to travel the same distance downstream.

Let the speed of the stream be \(x\) km/hr. 

1. Determine the effective speed downstream. This is the speed of the boat plus the speed of the stream:

\(S_{\text{down}} = 5 + x\) km/hr.

1. Determine the effective speed upstream. This is the speed of the boat minus the speed of the stream:

\(S_{\text{up}} = 5 - x\) km/hr.

1. According to the problem, the time taken to go 20 km upstream is thrice the time taken to go the same distance downstream. Using the formula \(\text{Time} = \frac{\text{Distance}}{\text{Speed}}\), we have:

\(\frac{20}{5 - x} = 3 \times \frac{20}{5 + x}\)

1. Simplify the equation:

Cross-multiply to eliminate the fractions:

\(20 \times (5 + x) = 3 \times 20 \times (5 - x)\)

Expand both sides:

\(100 + 20x = 300 - 60x\)

1. Rearrange the terms to isolate \(x\):

\(20x + 60x = 300 - 100\)

\(80x = 200\)

1. Solve for \(x\):

\(x = \frac{200}{80}\)

\(x = 2.5\) km/hr

Therefore, the speed of the stream is 2.5 km/hr.