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

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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

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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.

 


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