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 Gwalitor and Delhi. If speed of Aman is 30km/hr, what is the speed (in km/hr) of Kapil?

Options

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

Answer

To find the speed of Kapil, we can follow these steps:

### Step 1: Understand the problem
Aman and Kapil start from Delhi and Gwalior respectively and meet at Mathura. After meeting, Aman takes 196 minutes to reach Gwalior, and Kapil takes 225 minutes to reach Delhi.

### Step 2: Convert time from minutes to hours
Since speed is given in km/hr, we need to convert the time taken by Aman and Kapil from minutes to hours:
- Aman: \( 196 \text{ minutes} = \frac{196}{60} \text{ hours} \)
- Kapil: \( 225 \text{ minutes} = \frac{225}{60} \text{ hours} \)

### Step 3: Calculate the distance Aman travels after meeting
Aman's speed is given as 30 km/hr. The distance he travels after meeting Kapil can be calculated using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
So, the distance Aman travels after meeting is:
\[ P = 30 \times \frac{196}{60} = 30 \times \frac{49}{15} = 98 \text{ km} \]

### Step 4: Set up the equation for Kapil's distance
Let the speed of Kapil be \( x \) km/hr. The distance Kapil travels after meeting Aman is:
\[ Q = x \times \frac{225}{60} = x \times \frac{15}{4} \]

### Step 5: Establish the relationship between distances
Since both distances \( P \) and \( Q \) are the distances from Mathura to Gwalior and Mathura to Delhi respectively, we can set up the equation:
\[ P = Q \]
Substituting the values we have:
\[ 98 = x \times \frac{15}{4} \]

### Step 6: Solve for \( x \)
Now, we can solve for \( x \):
\[ x = \frac{98 \times 4}{15} = \frac{392}{15} \approx 26.13 \text{ km/hr} \]

### Step 7: Finalize the answer
Thus, the speed of Kapil is approximately \( 26.13 \) km/hr.