A boy goes to school from his home at a speed of 4 km/hr and returns at a speed of 6km/hr . If in total he took 5 hours in going and coming back, the distance between his house and school ?

Options

A. 8 km
B. 10 km
C. 12 km
D. 14 km

Explanation

To solve the problem step by step, we need to find the distance between the boy's house and school based on the given speeds and total time taken.

### Step-by-Step Solution:

1. **Define the Variables**:
Let the distance between the boy's house and school be \( d \) kilometers.

2. **Calculate Time Taken for Each Journey**:
- The time taken to go to school at a speed of 4 km/hr is given by the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{d}{4} \text{ hours} \]
- The time taken to return home at a speed of 6 km/hr is:
\[ \text{Time} = \frac{d}{6} \text{ hours} \]

3. **Set Up the Equation for Total Time**:
According to the problem, the total time taken for the round trip is 5 hours. Therefore, we can write the equation:
\[ \frac{d}{4} + \frac{d}{6} = 5 \]

4. **Find a Common Denominator**:
The least common multiple of 4 and 6 is 12. We will convert the fractions:
\[ \frac{d}{4} = \frac{3d}{12} \quad \text{and} \quad \frac{d}{6} = \frac{2d}{12} \]

5. **Combine the Fractions**:
Now we can combine the fractions:
\[ \frac{3d}{12} + \frac{2d}{12} = \frac{5d}{12} \]
So, the equation becomes:
\[ \frac{5d}{12} = 5 \]

6. **Solve for \( d \)**:
To isolate \( d \), multiply both sides by 12:
\[ 5d = 60 \]
Now, divide both sides by 5:
\[ d = 12 \]

7. **Conclusion**:
The distance between the boy's house and school is \( 12 \) kilometers.