CAT 2018 Quant Questions

Question:
On a long stretch of east-west road, A and B are two points such that B is 350 km west of A. One car starts from A and another from B at the same time. If they move towards each other, then they meet after 1 hour. If they both move towards east, then they meet in 7 hrs. The difference between their speeds, in km per hour, is

Show Answer
Correct Answer: 50

Let 'x' and 'y' be the speed (in km/hr) of cars starting from both A and B respectively.
If they both move in east direction, then B will overtake A only if y > x.
Also, relative speed of both the cars when they move in east direction = (y - x) km/hr
It is mentioned that they take 7 hours to meet. i.e. they travel 350 km in 7 hours with a relative speed of (y-x) km/hr.
Hence, (y - x) = 350/7 = 50 km/hr.

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