CAT 2018 Slot 1 QA Question 1: 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

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

Accepted Answer

Let Partha take t hours to travel from A to B.
Then Narayan takes $t - 4$ hours.
Partha reaches the midpoint in $\dfrac{t}{2}$ hours.
Given: $\dfrac{t}{2} = (t - 4) - 2$
$\dfrac{t}{2} = t - 6$
$t = 12$
So, Partha takes 12 hours to travel 60 km.
Speed of Partha $=\dfrac{60}{12} = 5$ km/hr.

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