Question : Suraj starts his journey from point Q at 2 pm. He drives the car at the speed of 40 km/hr for the first three hours and completes the remaining journey at the speed of 30 km/hr. If Rahul starts moving towards Suraj at 6 pm from point Q at the speed of 80 km/hr, then at what time he will catch Suraj?
Option 1: 9: 00 pm
Option 2: 9: 15 pm
Option 3: 9: 36 pm
Option 4: 10: 06 pm
Correct Answer: 9: 00 pm
Solution :
Given: Suraj starts his journey from point Q at 2 pm.
The Suraj's speed for the first 3 hours is 40 km/hr and completes the remaining journey at the speed of 30 km/hr.
Rahul's speed is 80 km/hr.
$\text{Time}=\frac{\text{Distance}}{\text{Speed}}$
The distance Suraj traveled until 6 pm = 3 × 40 + 30 = 120 + 30 = 150 km.
The relative speed between Rahul and Suraj = 80 – 30 = 50 km/hr.
Time = $\frac{150}{50}$ = 3 hours
Rahul will catch Suraj by 6 + 3 = 9: 00 pm.
Hence, the correct answer is 9: 00 pm.
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