CAT 2018 Slot 1 QA Question & Solution
Question
The distance from A to B is 60 km. Partha and Narayan start from A at the same time and move towards B. Partha takes four hours more than Narayan to reach B. Moreover, Partha reaches the mid-point of A and B two hours before Narayan reaches B. The speed of Partha, in km per hour, is
Options
Solution
Let the time taken by Partha to cover 60 km be x hours.
Narayan will cover 60 km in x-4 hours.
Speed of Partha = $\frac{60}{x}$
Speed of Narayan = $\frac{60}{x-4}$
Partha reaches the mid-point of A and B two hours before Narayan reaches B.
=> $\dfrac{30}{\frac{60}{x}} + 2 = \dfrac{60}{\frac{60}{(x-4)}}$
$\frac{x}{2} + 2 = x-4$
$\frac{x+4}{2}=x-4$
$x+4=2x-8$
$x=12$
Partha will take 12 hours to cross 60 km.
=> Speed of Partha = $\frac{60}{12}=5$ Kmph.
Therefore, option D is the right answer.