CAT 2023 Question Paper | Quant Slot 2

CAT Questions

CAT 2023 Quant was dominated by Algebra followed by Arithmetic. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 11 : 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

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Video Explanation

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Explanatory Answer

The speeds of Ravi and Ashok converted to meters per second are \( 40 \times \frac { 5 } { 18 } = \frac { 100 } { 9 } \mathrm {~m} / \mathrm { s } \) and \( 50 \times \frac { 5 } { 18 } = \frac { 125 } { 9 } \mathrm {~m} / \mathrm { s } \) respectively.

Let M be the meeting point between Ravi and Ashok.

The relative speed between Ravi and Ashok = \( \frac { 100 } { 9 } + \frac { 125 } { 9 } = \frac { 225 } { 9 } \mathrm {~m} / \mathrm { s } \)
So they meet exactly after \( \frac { 225 } { \frac { 225 } { 9 } } = 9 \) seconds.
The distance covered by R in 9 seconds = \( \frac { 100 } { 9 } \times 9 = 100 \mathrm {~m} \).
So, for all three of them to meet at the same time Vijay has to cover 54 + 100 = 154m in 9 seconds.
∴ The speed of Vijay = \( \frac { 154 } { 9 } \mathrm {~m} / \mathrm { s } = \frac { 154 } { 9 } \times \frac { 18 } { 5 } = 61.6 \mathrm { kmph } \)

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The question is " 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 "

The answer is '61.6'

Choice D is the correct answer.