Ranjeet leaves town P for town Q at 8:30 a.m., and Devsena leaves town Q for town P at 12:30 p.m. on the same road. The distance between the towns is 837 km. If Ranjeet's speed is 63 km/hr and Devsena's speed is 54 km/hr, at what time will they meet?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 5:30 p.m.
Until Devsena starts, only Ranjeet moves. After 12:30 p.m. the gap closes at the sum of the two speeds.
8:30 a.m. to 12:30 p.m. \(=4\) hours; Ranjeet covers \(4\times63=252\) km
Gap at 12:30 p.m. \(=837-252=585\) km
Closing speed \(=63+54=117\) km/hr
Time to meet \(\displaystyle =\frac{585}{117}=5\) hours after 12:30 p.m., that is 5:30 p.m.
They meet at 5:30 p.m.