Two boys A and B start at the same time to ride from Delhi to Meerut, 60 km away. A rides 4 km/h slower than B. B reaches Meerut and at once turns back meeting A at a place 12 km from Meerut. Find the speed of A.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 8 km/h
Both boys ride for the same time until they meet, so the distances they cover are in the ratio of their speeds.
A meets B 12 km before Meerut, so A has ridden \(60-12=48\) km
B rode 60 km to Meerut and 12 km back: \(60+12=72\) km
Let A’s speed be \(v\) km/h; B’s is \(v+4\)
Equal times: \(\displaystyle\frac{48}{v}=\frac{72}{v+4}\)
\(48v+192=72v\), so \(24v=192\) and \(v=8\)
Shortcut: The distances are in the ratio \(48:72=2:3\), so the speeds are too.
The speeds differ by 1 part of this ratio, and that part is 4 km/h
A’s speed is 2 parts \(=8\) km/h