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CAT 2020 Slot 3 — QA Question 2

Relative SpeedEasy

A and B are two railway stations 90 km apart. A train leaves A at 9:00 am, heading towards B at a speed of 40 km/hr. Another train leaves B at 10:30 am, heading towards A at a speed of 20 km/hr. The trains meet each other at

Answer & solution

Correct answer: 11 a.m.

  • A

    11:45 a.m.

  • 11 a.m.

  • C

    10:45 a.m.

  • D

    11:20 a.m.

Solution

Easy

The first train has a head start. Find how much of the 9090 km is already covered when the second train departs, then treat the rest as a standard "closing the gap" problem with the combined speed.

1

Head start of train from AA. It leaves at 9:009{:}00 and the train from BB leaves at 10:3010{:}30, a gap of 1.51.5 hours at 4040 km/hr.

Distance=40×1.5⇒ Distance=60 km\begin{aligned} &\text{Distance}=40\times1.5\\ &\Rightarrow\ \text{Distance}=60\text{ km} \end{aligned}
2

Gap remaining at 10:3010{:}30.

Gap=90−60(from step 1)⇒ Gap=30 km\begin{aligned} &\text{Gap}=90-60 \quad\text{(from step 1)}\\ &\Rightarrow\ \text{Gap}=30\text{ km} \end{aligned}
3

Time to close the gap. Now both move toward each other, so speeds add: 40+20=6040+20=60 km/hr.

t=3040+20=3060⇒ t=0.5 hr=30 min\begin{aligned} &t=\frac{30}{40+20}=\frac{30}{60}\\ &\Rightarrow\ t=0.5\text{ hr}=30\text{ min} \end{aligned}

So they meet 3030 minutes after 10:3010{:}30, i.e. at 11:0011{:}00 a.m.

11:00 a.m.11{:}00\ \text{a.m.}

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CAT 2020 Slot 3 QA Q2: A and B are two railway stations 90 km apart. A train leaves A at 9:00 am, heading towards B at a speed of 40 — Solution | TheCATExam