CAT 2018 Question Paper | Quants Slot 1

CAT Questions

This is an actual question from CAT 2018 Question Paper based on the topic Speed and Distance. This is one of those easy questions that you don't want to miss out. Practicing many such questions from CAT Previous Year Paper is the best way to gear up for the CAT Exam.Start right away!

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 between X and Z is three-fifths of that between X and Y. How many hours does train T take for its journey from X to Y? [TITA]

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Video Explanation

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Explanatory Answer

Method of solving this CAT Question from Speed Time Distance

From question, XZ = 3d, YZ = 2d
As their speeds are in ratio 4:3
Let their speeds be 4V and 3V
Time (T to reach Z) = $\frac{3𝑑}{4𝑣}$ hrs ---(1)
Time (S to reach Z) = $\frac{2𝑑}{3𝑣}$ hrs ---(2)

We need to find the time taken for T To travel from X to Y
Time = $\frac{5d}{4v}$
Train S started one hour late than Train T
=> $\frac{3𝑑}{4𝑣}$ - 1 = $\frac{2𝑑}{3𝑣}$

Let $\frac{d}{v}$ = k
$\frac{3}{4}$k - $\frac{2}{3}$k = 1
k = 12
So, $\frac{5𝑑}{4𝑣}$ = $\frac{5 × 12}{4}$ = 15 hours

The question is "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 between X and Z is three-fifths of that between X and Y. How many hours does train T take for its journey from X to Y? [TITA]"

Hence, the answer is 15 hours

 

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