CAT 2025 Slot 3 QA Question 18: Two places A and B are 45 kms apart and connected by a straight road. Anil goes from A to B while Sunil goes from B to A. Starting at the same time, they cross each other in exactly 1 hour 30 minutes.

Question

Two places A and B are 45 kms apart and connected by a straight road. Anil goes from A to B while Sunil goes from B to A. Starting at the same time, they cross each other in exactly 1 hour 30 minutes.

Accepted Answer

Let Anil’s speed be $u$ km/hr and Sunil’s speed be $v$ km/hr.
They meet after $1.5$ hours over a distance of $45$ km.
$u + v = \dfrac{45}{1.5} = 30$
Anil reaches $1.25$ hours after Sunil, so Anil is slower.
$\dfrac{45}{u} - \dfrac{45}{v} = 1.25$
Using $v = 30 - u$:
$\dfrac{45(30 - 2u)}{u(30 - u)} =