P and R are at a distance of 296 km from each other at 7:45 a.m. After 15 minutes, P starts moving towards R at the speed of 32 km/hr. At 8:30 a.m. R starts moving towards P at the speed of 8 km/hr. At what time will they meet?

Correct option is A

Given:
Distance between P and R = 296 km
P starts moving at 8:00 a.m. towards R at 32 km/h.
R starts moving at 8:30 a.m. towards P at 8 km/h.
P and R are at a distance of 296 km from each other at 7:45 a.m.

Formula Used:
Time = $$\frac{\text{Distance}}{\text{Relative Speed}}$$

Meeting Time = Start Time + $$\frac{\text{Remaining Distance}}{\text{Relative Speed}}$$​​

Solution:
P travels alone from 8:00 a.m. to 8:30 a.m. = 0.5 hours
Distance = $$32 \times 0.5 = 16$$ km
Remaining distance at 8:30 a.m.
296 - 16 = 280 km
Relative speed = 32 + 8 = 40 km/hr
Time to meet =$$\frac{280}{40} = 7$$  hours
Meeting time = 8:30 a.m. + 7 hours = 3:30 p.m.
The time when P and R meet is 3:30 p.m.
Thus, the correct option is (a) 3:30 pm
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