Question

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

• A. 67.2
• B. 64.4
• C. 61.6
• D. 58.8

Answer 1

The Correct Option is C

It is said that Ravi travels at a speed of 40 kmph, or\(\frac{ 100}{9}\) meters / second.
In addition, Ashok's speed is known to be 50 kmph, or \(\frac{125}{9}\) m/s. It is known that there are 225 meters separating Ravi and Ashok, and that their respective velocities are \(\frac{125}{9} + \frac{100}{9} = 25 \, \text{m/s}\)
As a result, they will cross paths in \(\frac{225 }{ 25} = 9\) seconds. 
In these nine seconds, Ravi covered a distance of \(\frac{100 }{9} × 9 = 100\) meters.
Vijay had to cover\( (100+54) = 154\) meters in these 9 seconds since he was already 54 meters behind Ravi when they started.
Accordingly, Vijay's speed is \(\frac{154 }{ 9}\) m/s, or 
\(\frac{154}{9} \times \frac{18}{5} = \frac{308}{5}\)
\(=61.6\) kmph.
The correct option is (C): 61.6