CAT 2020 Slot 1 QA Q7 Time, Speed & Distance

Question 7 of the Quantitative Ability (QA) section, CAT 2020 Slot 1, with CAT's official answer and a worked solution.

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. A
    90
  2. B
    80
  3. C
    70
  4. D
    100

Answer: (A) 90 Time, Speed & Distance MCQ

Solution

  1. After meeting, the times left \(t_1=45\), \(t_2=20\) satisfy \(\frac{v_2}{v_1} = \sqrt{\frac{t_1}{t_2}}\).
  2. \(\frac{v_2}{60} = \sqrt{\frac{45}{20}} = \frac32 \Rightarrow v_2 = 90\) km/h.

Shortcut. Speed ratio after meeting = square root of the inverse ratio of remaining times.

Same concept in other years

See every question on After meeting, speed ratio = √(ratio of remaining times).

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