Question : A leaves station P at 8:00 a.m. and reaches station Q at 11:00 a.m. B leaves Station Q at 9:00 a.m. and reaches Station P at 11:00 a.m. At what time will they cross each other?
Option 1: 10:00 a.m.
Option 2: 10:05 a.m.
Option 3: 9:48 a.m.
Option 4: 9:52 a.m.
Correct Answer: 9:48 a.m.
Solution :
A leaves station P at 8:00 a.m. and reaches station Q at 11:00 a.m
⇒ Time taken by A = 3 hrs
B leaves Station Q at 9:00 a.m. and reaches Station P at 11:00 a.m
⇒ Time taken by B = 2 hrs
Let the distance between P and Q = 6$x$ km
So, Speed of A = $\frac{6x}{3}$ = 2$x$ km/h
and Speed of B = $\frac{6x}{2}$ = 3$x$ km/h
Relative speed = 2$x$ + 3$x$ = 5$x$ km/h
Distance covered by A in 1hr = 2$x$ × 1 = 2$x$ km
Remaining distance = 4$x$ km
Time taken to cross each other after 9 a.m.
= $\frac{4x}{5x}$hr = $\frac{4x}{5x}$ × 60 = 48 minutes
Hence, the correct answer is 9:48 a.m.
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