CAT 2023 Question Paper | Quant Slot 2

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

Video Explanation

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 = $\frac { 154 } { 9 } \mathrm {~m} / \mathrm { s } = \frac { 154 } { 9 } \times \frac { 18 } { 5 } = 61.6 \mathrm { kmph }$

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.

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