# CAT Quantitative Aptitude Questions | CAT Time Speed and Distance & Races

###### CAT Questions | Speed Time | Relative Speed

The question is from the topic Relative Speed. This is a classic CAT level question testing your understanding in the concept of relative speed from Time Speed and Distance. Time Speed and Distance is a favorite in CAT Exam and appears more often than expected in the CAT Quantitative Aptitude section in the CAT Exam

Question 27 : Two trains left from two stations P and Q towards station Q and station P respectively. 3 hours after they met, they were 675 Km apart. First train arrived at its destination 16 hours after their meeting and the second train arrived at its destination 25 hours after their meeting. How long did it take for the first train to make the whole trip?

1. 18h
2. 36h
3. 25h
4. 48h

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##### Method of solving this CAT Question from Time Speed Distance: Let's start with creating a visual of how the trains cross each other.

Total distance travelled by both the trains before meeting = D. This distance will be covered in the proportion of their speeds. Clarify with the diagram.

3 hours after meeting distance travelled by A = SA * 3 and by B = SB * 3
Therefore, 3 (SA + SB) = 675 => SA + SB = 225.

Now the remaining distance to be covered by first train is DSB/(SA + SB)
Therefore, time taken = $$frac{DS_{B}}{$S_{A} + S_{B}$S_{A}}$ = 16 ---------$1)
Similarly, $$frac{DS_{A}}{$S_{A} + S_{B}$S_{A}}$ = 25 ---------$2)

Dividing equation 1 by 2 -

$$frac{S_A^2}{S_B^2}\\$ = $\frac{25}{16}\\$ => $\frac{S_A}{S_B}\\$ = $\frac{5}{4}\\$. Therefore, SA + $\frac{4}{5}\\$ * SA = 225 => SA = 125 Km/hr and SB = 100 Km/hr From equation 2, $\frac{D}{S_A}\\$ = 16 * $\frac{225}{100}\\$ = 36h, which is the time taken for the first train to complete the journey. The question is "How long did it take for the first train to make the whole trip?" ##### Hence,it took 36h for the first train to make the whole trip. Choice B is the correct answer. ###### 2IIM's Online CAT CoachingGet CAT Last Mile Prep Course for 799 /- Signup Now! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2020Enroll at 44,000/- Next Weekend Batch Starts Sat, Nov 2nd, 2019 ###### Best CAT Coaching in ChennaiRegister Online, get Rs 4000/- off Attend a Demo Class ## CAT Preparation Online | CAT Arithmetic Videos On YouTube #### Other useful sources for Arithmetic Question | Time Speed Distance and Races Sample Questions ##### 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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