CAT 2020 Question Paper | Quants Slot 1

CAT Previous Year Paper | CAT Quants Questions | Question 7

This question is from Speed time distance. Speed time distance is a favorite topic in CAT Exam. Questions from speed time distance have appeared consistently in the CAT exam for the last several years. CAT exam is known for not checking for formulaic knowledge but for strong fundamentals and application of the concepts involved. This question is something like that.

Question 7 : A straight road connects points A and B. Car 1 travels from A to B and Car 2 travels from B to A, both leaving at the same time. After meeting each other, they take 45 minutes and 20 minutes, respectively, to complete their journeys. If Car 1 travels at the speed of 60 km/hr, then the speed of Car 2, in km/hr, is

  1. 90
  2. 80
  3. 70
  4. 100

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Explanatory Answer

Let the meeting point be D. Let’s assume C1 takes t minutes to reach the meeting point. Then C2 takes same t minutes to reach the meeting point. Graphs showing translations of mod of x After reaching the destinations...
C1 takes t minutes to cover AD, while C2 takes 20 minutes
C1 takes 45 minutes to cover DB, while C2 takes t minutes

the ratio of speeds of C1 and C2 on the stretch AD will be equal to the ratio of their speed on the stretch DB.
When the distances are the same, the ratio of speeds is the inverse ratio of time taken.
ratio of speeds of C1 and C2 on the stretch AD = \\frac{20}{t})
ratio of speeds of C1 and C2 on the stretch DB = \\frac{t}{45})
Therefore, \\frac{20}{t}) = \\frac{t}{45})
t × t = 45 × 20
t 2 = 900
t = 30.

\\frac{Speed of C1}{Speed of C2}) = \\frac{20}{t})
\\frac{60}{Speed of C2}) = \\frac{20}{30})
Speed of C2 = 90 kmph

The answer is, "90"

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