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

CAT Questions | Speed Time | Races

The question is from the topic of Time Speed and Distance. This question tests the understanding of questions under meeting points template. 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 18: Tom, Jerry and Bill start from point A at the same time in their cars to go to B. Tom reaches point B first and turns back and meets Jerry at a distance of 9 miles from B. When Jerry reaches B, he too turns back and meets Bill at a distance of 7 miles from B. If 3 times the speed with which Tom drives his car is equal to 5 times Bill’s speed, what could be the distance between the points A and B?

  1. 40 miles
  2. 24 miles
  3. 31 miles
  4. 63 miles

Rs. 2500 off on 2IIM Ultimate DI LR Course for CAT 2019. Offer valid till March 24th.

Signup to sample the Best CAT Online Coaching

Best CAT Coaching in Chennai

Starts Sat, Mar 23, 2019

Explanatory Answer

Method of solving this CAT Question from Time Speed Distance: Find the ratio of Tom's and Jerry's speed. Similarly find the ratio of Jerry's and Bill's speed. Given to us is the ratio of Tom's and Bill's speed. Combine all to find the distance!

Let the distance between A and B be ‘x’ miles.
Let their speeds be T, J and B in miles/hour

When Tom meets Jerry:
Distance travelled by Tom = x + 9
Distance travelled by Jerry = x – 9
Time taken will be the same => \\frac{x+9}{T}\\) = \\frac{x-9}{J}\\)
Or \\frac{T}{J}\\) = \\frac{x+9}{x-9}\\) --(1)

When Jerry meets Bill:
Distance travelled by Jerry = x + 7
Distance travelled by Bill = x – 7
Time taken will be the same => \\frac{x+7}{J}\\) = \\frac{x-7}{B}\\)
Or \\frac{J}{B}\\) = \\frac{x+7}{x-7}\\) --(2)

Given 3T = 5B
or \\frac{T}{B}\\) = \\frac{5}{3}\\)
From (1) and (2)
\\frac{T}{B}\\) = \\frac{T}{J}\\) * \\frac{J}{B}\\)
5(x - 9)(x - 7) = 3 (x + 9)(x + 7)
5x2 – 80x + 315 = 3x2 + 48x + 189
2x2 – 128x + 126 = 0
x2 – 64x + 63 = 0
x = 63 or x = 1

The question is " What could be the distance between the points A and B?"
Therefore, X has to be 63.

Hence, the answer is 63 miles.

Choice D is the correct answer.


Online CAT Coaching
Try it free!

Register in 2 easy steps and start learning in 30 seconds!

★ Sign up for Free

Already have an Account?

★ Login to Continue

CAT Coaching in Chennai

Next Weekend Batch Starts Sat, Mar 23rd, 2019

★ CAT Coaching Info

Best CAT Coaching in Chennai

Sign up for a Free Demo of our CAT Coaching in Chennai

★ Schedule Demo

CAT Preparation Online | CAT Arithmetic Videos On YouTube

Other useful sources for Arithmetic Question | Time Speed Distance and Races Sample Questions

CAT Questions | CAT Quantitative Aptitude

CAT Questions | CAT DILR

CAT Questions | Verbal Ability for CAT

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
Mobile: (91) 99626 48484
WhatsApp: WhatsApp Now