CAT 2020

Slot 1

QA

Question & Solution

Let the speed of Car 2 be 'x' kmph and the time taken by the two cars to meet be 't' hours.

In 't' hours, Car 1 travels $\left(60\ \times\ t\right)\ km$ while Car 2 travels $\left(x\ \times\ t\right)\ km$

It is given that the time taken by Car 1 to travel $\left(x\ \times\ t\right)\ km$ is 45 minutes or (3/4) hours.

$\therefore\ \frac{\left(x\ \times\ t\right)}{60}\ =\ \frac{3}{4}$ or $t=\frac{180}{4x}$..................................(i)

Similarly, the time taken by Car 2 to travel $\left(60\ \times\ t\right)\ km$ is 20 minutes or (1/3) hours.

$\therefore\ \frac{\left(60\times\ t\right)}{x}=\frac{1}{3}$ or $\therefore\ t=\frac{x}{180}$.............................(ii)

Equating the values in (i) and (ii), and solving for x:

$\therefore\ \frac{180}{4x}=\frac{x}{180}\ \ \longrightarrow\ \ \ x\ =90\ kmph$

Hence, Option B is the correct answer.