A man can go downstream thrice as fast as he can go upstream between two specific points on a river. If the river flows at 8 kmph, what is the speed of the boat in still water?
- 14 kmph
- 15 kmph
- 16 kmph
- 18 kmph
The Correct Option is C
Solution and Explanation
To solve the problem, we need to find the speed of the boat in still water. Let's denote the speed of the boat in still water as \(b\) kmph. We are given:
- Downstream speed = \(b + 8\) kmph (where 8 kmph is the speed of the river)
- Upstream speed = \(b - 8\) kmph
According to the problem, the downstream speed is three times the upstream speed:
\(b + 8 = 3(b - 8)\)
This equation arises from the relation between the downstream and upstream speeds.
Simplifying the equation:
\(b + 8 = 3b - 24\)
\(b - 3b = -24 - 8\)
\(-2b = -32\)
Dividing both sides by -2 gives:
\(b = 16\)
Therefore, the speed of the boat in still water is 16 kmph.
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