Car A, travelling at 60kmph leaves City X for City Y at 5pm

Car A, travelling at 60kmph leaves City X for City Y at 5pm. Car B leaves city X for City Y at 7pm and travels at 100 kmph. When will Car B overtake Car A?

A) 9:45 p.m
B) 9:55 p.m
C) 10:00 p.m
D) 10:05 p.m
E7:55 p.m

Solution:
Questions related to overtaking in Time Speed and Distance are considered one of the most confusing ones in Quant. However, there is a pretty simple method to follow for solving such questions. The step by step guide is as follows:

Step 1:
Calculate the distance travelled by the vehicle that started early, by the time the second vehicle starts. Now that is the lag time that has to be covered by the vehicle starting late in order to overtake the first one.

Time elapsed between the start of Car A and B = 2 hours

Distance covered by Car A in 2 hours => Distance = Speed * Time
=> Distance = 60 * 2 = 120km

Step 2:
Car B will overtake Car A as soon as it covers the distance of 120km, with the relative speed of both the cars.

Relative speed of Car A and Car B (moving in same direction)
= Speed of car B – Speed of Car A.
= 100 – 60
= 40kmph

Step 3: Now Time taken by Car B to overtake Car A, with a relative speed of 40kmph
= 120 / 40
=> 3 hours

Thus Car B would overtake Car A after 3 hours from the time Car B started, i.e. at 10pm

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