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CAT 2021 Slot 1 QA Question & Solution

ArithmeticEasy

Question

Two trains cross each other in 14 seconds when running in opposite directions along parallel tracks. The faster train is 160 m long and crosses a lamp post in 12 seconds. If the speed of the other train is 6 km/hr less than the faster one, its length, in m, is

Options

184
192
190
180

Solution

Speed of the faster train = $\frac{160}{12} = \frac{40}{3} $ m/s

Speed of the slower train = $\frac{40}{3}-\left(6\times\ \frac{5}{18}\right)=\frac{35}{3}$ m/s

Sum of speeds (when the trains travel towards each other) = $\frac{40}{3}+\frac{35}{3}=25$ m/s

Let the slower train be $x$ metres long; then: $\frac{160+x}{25}=14$

On solving, $x=190\ m$