# CAT 2018 Question Paper | Quants Slot 1

###### CAT Previous Year Paper | CAT Speed Time Distance Questions | Question 23

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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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##### 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 ###### ⏰ Last Intake for CAT '21 Crash course! Buy now for just Rs. 8000. Valid until 27th Sep ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2021Enroll at 49,000/- 44,000/- Online Classroom Batches Starting Now! ###### Best CAT Coaching in Chennai Introductory offer of 5000/- Attend a Demo Class ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
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