CAT 2018 Slot 1 QA Question 23: Train T leaves station X for station Y at 3 pm. Train S, traveling at three quarters of the speed of T, leaves Y for X at 4 pm. The two trains pass each other at a station Z, where the distance betwee

Question

Train T leaves station X for station Y at 3 pm. Train S, traveling at three quarters of the speed of T, leaves Y for X at 4 pm. The two trains pass each other at a station Z, where the distance betwee

Accepted Answer

Let the total distance XY be D and the speed of train T be v.
Let T take T0 hours for the full journey. Then $T_{0} = \dfrac{D}{v}$.
Train T travels $\dfrac{3D}{5}$ before meeting, so the meeting time after 3 pm is
$\dfrac{3D}{5v} = \dfrac{3T_{0}}{5}$
Train S starts one hour later and travels $\dfra