Two towns, Rampur and Sitapur, are 60 km apart on the same river, with Sitapur downstream of Rampur. At the same moment, one boat leaves Rampur for Sitapur and another boat leaves Sitapur for Rampur. Each boat moves at 12 km/hr in still water, and the river flows at 3 km/hr. How far from Rampur do the two boats meet?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 37.5 km
The boat from Rampur goes downstream and the boat from Sitapur goes upstream. They move towards each other, so the gap closes at the sum of their speeds.
Boat from Rampur (downstream): \(12+3=15\) km/hr
Boat from Sitapur (upstream): \(12-3=9\) km/hr
The gap closes at \(15+9=24\) km/hr
Time to meet \(\displaystyle =\frac{60}{24}=2.5\) hours
Distance from Rampur \(=15\times2.5=37.5\) km
Check: the other boat goes \(9\times2.5=22.5\) km, and \(37.5+22.5=60\) km