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

Provided data:

• Ravi's velocity: 40 km/h, equivalent to \( \frac{100}{9} \) m/s.
• Ashok's velocity: 50 km/h, equivalent to \( \frac{125}{9} \) m/s.
• Initial separation between Ravi and Ashok: 225 meters.

Step 1: Combined Velocity Calculation

The relative velocity of Ravi and Ashok when approaching each other is the sum of their individual velocities:

\[ \text{Combined Velocity} = \frac{125}{9} + \frac{100}{9} = 25 \, \text{m/s} \]

Step 2: Time to Meet Calculation

The time until they meet is determined by the distance and their combined velocity:

\[ \text{Time} = \frac{\text{Distance}}{\text{Relative Velocity}} = \frac{225}{25} = 9 \, \text{seconds} \]

Step 3: Ravi's Distance Traveled

In 9 seconds, Ravi covers the following distance:

\[ \text{Distance} = \frac{100}{9} \times 9 = 100 \, \text{meters} \]

Step 4: Vijay's Total Distance Requirement

Vijay begins 54 meters behind Ravi. Consequently, Vijay must cover a total distance of:

\[ \text{Distance} = 100 + 54 = 154 \, \text{meters} \]

Step 5: Vijay's Velocity Calculation

Vijay's velocity is calculated as:

\[ \text{Velocity} = \frac{154}{9} \, \text{m/s} \]

The conversion of Vijay's velocity to kilometers per hour is as follows:

\[ \text{Velocity} = \frac{154}{9} \times \frac{18}{5} = \frac{308}{5} = 61.6 \, \text{km/h} \]

Conclusion

Therefore, Vijay's velocity is \( \textbf{61.6 km/h} \).

The correct option is \( \textbf{(C): 61.6} \).