CAT 2023 Slot 2 QA Q11 Time, Speed & Distance

Question 11 of the Quantitative Ability (QA) section, CAT 2023 Slot 2, with CAT's official answer and a worked solution.

Ravi is driving at a speed of 40 km/h on a road. Vijay is 54 meters behind Ravi and driving in the same direction as Ravi. Ashok is driving along the same road from the opposite direction at a speed of 50 km/h and is 225 meters away from Ravi. The speed, in km/h, at which Vijay should drive so that all the three cross each other at the same time, is
  1. A
    58.8
  2. B
    64.4
  3. C
    67.2
  4. D
    61.6

Answer: (D) 61.6 Time, Speed & Distance MCQ

Solution

  1. Ravi and Ashok approach each other at \(40 + 50 = 90\) km/h across 225 m, so they meet after \(\frac{0.225}{90} = 0.0025\) h (9 seconds).
  2. In that time Ravi covers \(40 \times 0.0025 = 0.1\) km \(= 100\) m.
  3. Vijay must reach the same point, covering \(54 + 100 = 154\) m in 0.0025 h.
  4. Speed \(= \frac{0.154}{0.0025} = 61.6\) km/h.

Shortcut. Relative to Ravi: Vijay closes 54 m in the time Ashok closes 225 m at 90 km/h, so \(v - 40 = 90\times\frac{54}{225} = 21.6\) and \(v = 61.6\).

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