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

We are given the following information:

• Ravi's speed = 40 km/h, which is equivalent to \( \frac{100}{9} \) meters per second.
• Ashok's speed = 50 km/h, which is equivalent to \( \frac{125}{9} \) meters per second.
• The distance between Ravi and Ashok = 225 meters. 

Step 1: Calculate Combined Velocity

The relative speed (combined velocity) of Ravi and Ashok when they move towards each other is the sum of their speeds:

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

Step 2: Time to Meet

The time taken for Ravi and Ashok to meet is calculated using the formula:

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

Step 3: Distance Covered by Ravi

In these 9 seconds, Ravi will cover:

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

Step 4: Distance Covered by Vijay

Vijay starts 54 meters behind Ravi. Therefore, Vijay needs to cover a total distance of:

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

Step 5: Calculate Vijay's Speed

Vijay's speed is calculated as:

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

Next, we convert Vijay's speed into kilometers per hour:

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

Conclusion

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

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