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

###### CAT Questions | Speed Time | Time and Distance

The question is from the topic Time and distance. It is a classic question involving the concept of speed, distance and time. 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 3: Three cars leave A for B in equal time intervals. They reach B simultaneously and then leave for Point C which is 240 km away from B. The first car arrives at C an hour after the second car. The third car, having reached C, immediately turns back and heads towards B. The first and the third car meet a point that is 80 km away from C. What is the difference between the speed of the first and the third car?

1. 60 kmph
2. 20 kmph
3. 40 kmph
4. 80 kmph

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##### Method of solving this CAT Question from Time Speed Distance: Create a visual of where the three cars are and how they travel between the points.

Let V1, V2 and V3 be the speeds of the cars.

$$frac{AB}{V_{1}}\\$ - $\frac{AB}{V_{2}}\\$ = $\frac{AB}{V_{2}}\\$ - $\frac{AB}{V_{3}}\\$ $\frac{240}{V_{1}}\\$ - $\frac{240}{V_{2}}\\$ = 1 V3 = 2V1 Condition I states that the cars leave in equal intervals of time and arrive at the same time. Or, the difference in the time taken between cars 1 and 2 should be equal to the time taken between cars 2 and 3. We get $\frac{AB}{V_{1}}\\$ - $\frac{AB}{V_{2}}\\$ = $\frac{AB}{V_{2}}\\$ - $\frac{AB}{V_{3}}\\$ As the second car arrived at C an hour earlier than the first, we get a second equation $\frac{240}{V_{1}}\\$ - $\frac{240}{V_{2}}\\$ = 1 The third car covered 240 + 80 kms when the first one covered 240 – 80 kms. Therefore, $\frac{320}{V_{3}}\\$ = $\frac{160}{V_{1}}\\$ This gives us V3 = 2V1 From condition 1, we have $\frac{AB}{V_{1}}\\$ - $\frac{AB}{V_{2}}\\$ = $\frac{AB}{V_{2}}\\$ - $\frac{AB}{V_{3}}\\$ Substituting V3 = 2V1, this gives us $\frac{AB}{V_{1}}\\$ - $\frac{AB}{V_{2}}\\$ = $\frac{AB}{V_{2}}\\$ - $\frac{AB}{2V_{1}}\\$ or $\frac{3AB}{2V_{1}}\\$ = $\frac{2AB}{V_{2}}\\$ or V2 = $\frac{4V_{1}}{3}\\$ Solving $\frac{240}{V_{1}}\\$ - $\frac{240}{V_{2}}\\$ = 1 , we get $\frac{60}{V_{1}}\\$ = 1 or V1 = 60 kmph => V2 = 80 kmph and V3 = 120 kmph The question is "What is the difference between the speed of the first and the third car?" ##### Hence, the answer is 60 kmph Choice A is the correct answer. ###### Best Online CAT CoachingSignup and sample5 classes for free Signup Now! ###### Already have an Account? ###### CAT Coaching in ChennaiEnroll at 29000/- Next Weekend Batch Starts Sat, June 29th, 2019 ###### Best CAT Coaching in ChennaiEarly Bird discount of 7000 Personalised attention, Small batch sizes. ## 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, 10-C, Kalinga Colony, Bobbili Raja Salai K.K.Nagar, Chennai. India. Pin - 600 078 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
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