A boat goes 42 km downstream from a ghat at Kishanpur to a ghat at Belapur. Without stopping, it turns back and goes 20 km upstream to a ghat at Devgarh, which lies between them. The whole journey takes 5 hours. The river flows at 2 km/hr. What is the speed of the boat in still water?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 12 km/hr
The downstream time and the upstream time together make 5 hours; both depend on the boat’s speed in still water.
Let the speed of the boat in still water be \(b\) km/hr; downstream \(=b+2\), upstream \(=b-2\)
\(\displaystyle \frac{42}{b+2}+\frac{20}{b-2}=5\)
\(42(b-2)+20(b+2)=5(b^{2}-4)\)
\(62b-44=5b^{2}-20\), that is \(5b^{2}-62b+24=0\)
\((b-12)(5b-2)=0\), so \(b=12\) or \(b=0.4\)
\(b=0.4\) is less than the river’s speed, so the boat could not go upstream; hence \(b=12\) km/hr
Check: \(42\div14=3\) hr and \(20\div10=2\) hr; \(3+2=5\) hr