Aman and Kapil start from Delhi and Gwalior respectively towards each other at the same time. They meet at Mathura and then take 196 minutes and 225 minutes respectively to reach Gwalior and Delhi. If speed of Aman is 30 km/hr, what is the speed (in km/hr) or Kapil ?

Options

A. 28
B. 30
C. `(225)/(7)`
D. `(392)/(15)`

Answer

To solve the problem, we will use the relationship between the speeds of Aman and Kapil and the times they took to reach their respective destinations after meeting at Mathura.

### Step-by-Step Solution:

1. **Identify Given Information:**
- Speed of Aman (V1) = 30 km/hr
- Time taken by Aman to reach Gwalior after meeting = 196 minutes
- Time taken by Kapil to reach Delhi after meeting = 225 minutes

2. **Convert Time from Minutes to Hours:**
- Time taken by Aman (T1) = 196 minutes = 196/60 hours = 3.27 hours (approximately)
- Time taken by Kapil (T2) = 225 minutes = 225/60 hours = 3.75 hours (approximately)

3. **Use the Speed Ratio Formula:**
- The formula relating the speeds and times is:
\[ \frac{V2}{V1} = \sqrt{\frac{T2}{T1}} \]
- Here, V2 is the speed of Kapil, and T1 and T2 are the times taken by Aman and Kapil respectively.

4. **Substitute the Values into the Formula:**
\[ \frac{V2}{30} = \sqrt{\frac{3.75}{3.27}} \]

5. **Calculate the Right Side:**
- First, calculate \(\frac{3.75}{3.27}\):
\[ \frac{3.75}{3.27} \approx 1.144 \]
- Now, take the square root:
\[ \sqrt{1.144} \approx 1.069 \]

6. **Solve for Kapil's Speed (V2):**
\[ V2 = 30 \times 1.069 \approx 32.07 \text{ km/hr} \]

7. **Final Answer:**
- The speed of Kapil is approximately 32.07 km/hr.