The distance between two places, A and B, is 300 km. Two riders, on scooters start simultaneously from A and B towards each other. The distance between them after 2.5 hrs is 25km. If the speed of one scooter is 10 km/hr more than the other find the speed of each scooter in km/hr.
A. 50 and 60
B. 30 and 40
C. 40 and 50
D. 60 and 70

Options

A. D
B. C
C. A
D. B

Answer

To solve the problem, we need to find the speeds of two scooters that are riding towards each other from two places, A and B, which are 300 km apart. Let's denote the speed of the first scooter as \( x \) km/hr and the speed of the second scooter as \( x + 10 \) km/hr (since one scooter is 10 km/hr faster than the other).

### Step 1: Set up the equation for distance traveled
After 2.5 hours, the total distance traveled by both scooters combined can be expressed as:
\[ \text{Distance traveled by first scooter} + \text{Distance traveled by second scooter} = \text{Total distance between A and B} - \text{Distance between them after 2.5 hours} \]
This gives us:
\[ 2.5x + 2.5(x + 10) = 300 - 25 \]

### Step 2: Simplify the equation
Now, simplify the equation:
\[ 2.5x + 2.5x + 25 = 275 \]
Combine like terms:
\[ 5x + 25 = 275 \]

### Step 3: Solve for \( x \)
Now, isolate \( x \) by subtracting 25 from both sides:
\[ 5x = 275 - 25 \]
\[ 5x = 250 \]
Now divide by 5:
\[ x = 50 \]

### Step 4: Find the speed of the second scooter
Now that we have \( x \), we can find the speed of the second scooter:
\[ \text{Speed of second scooter} = x + 10 = 50 + 10 = 60 \text{ km/hr} \]

### Conclusion
The speeds of the scooters are:
- First scooter: 50 km/hr
- Second scooter: 60 km/hr

Thus, the answer is:
**A. 50 and 60**