A train covers a distance between station A and station B in 45 minutes. If the speed of the train is reduced by 5km/hr, then the same distance is covered in 48 minutes. The distance between station A and B is

Options

A. 60km
B. 64km
C. 80km
D. 55km

Answer

To solve the problem, we need to find the distance between station A and station B using the information provided about the train's speed and travel time.

### Step-by-Step Solution:

1. **Define Variables:**
Let the speed of the train be \( S \) km/hr. The distance between stations A and B can be represented as \( D \) km.

2. **Convert Time to Hours:**
The time taken to cover the distance from A to B is given as 45 minutes. We need to convert this into hours:
\[ \text{Time in hours} = \frac{45}{60} = 0.75 \text{ hours} \]

3. **Write the Distance Equation for the First Scenario:**
Using the formula for distance, we have:
\[ D = S \times 0.75 \]

4. **Speed Reduction:**
If the speed is reduced by 5 km/hr, the new speed becomes \( S - 5 \) km/hr. The time taken to cover the same distance in this case is 48 minutes, which we convert to hours:
\[ \text{Time in hours} = \frac{48}{60} = 0.8 \text{ hours} \]

5. **Write the Distance Equation for the Second Scenario:**
For the second scenario, the distance can also be expressed as:
\[ D = (S - 5) \times 0.8 \]

6. **Set the Two Distance Equations Equal:**
Since both expressions represent the same distance \( D \), we can set them equal to each other:
\[ S \times 0.75 = (S - 5) \times 0.8 \]

7. **Expand and Rearrange the Equation:**
Expanding the right side:
\[ 0.75S = 0.8S - 4 \]
Rearranging gives:
\[ 0.75S - 0.8S = -4 \]
\[ -0.05S = -4 \]

8. **Solve for \( S \):**
Dividing both sides by -0.05:
\[ S = \frac{-4}{-0.05} = 80 \text{ km/hr} \]

9. **Calculate the Distance \( D \):**
Now that we have the speed, we can find the distance using the first distance equation:
\[ D = S \times 0.75 = 80 \times 0.75 = 60 \text{ km} \]

### Final Answer:
The distance between station A and station B is **60 km**.