Amit travelled a distance of 50 km in 9 hours. He travelled partly on foot at 5 km/h and partly by bicycle at 10 km/h. The distance travelled on the bicycle is:

Options

A. 12 m
B. 13 km
C. 10 km
D. 11 km

Answer

To solve the problem, we need to determine the distance Amit traveled by bicycle given the total distance he traveled and the speeds at which he traveled on foot and by bicycle.

### Step-by-Step Solution:

1. **Define Variables**:
Let \( x \) be the distance traveled on foot and \( y \) be the distance traveled by bicycle. According to the problem:
\[ x + y = 50 \quad \text{(1)} \]

2. **Determine Time Taken**:
The time taken to travel on foot and by bicycle can be expressed using the formula \( \text{Time} = \frac{\text{Distance}}{\text{Speed}} \).
- Time taken on foot:
\[ \text{Time}_{\text{foot}} = \frac{x}{5} \quad \text{(2)} \]
- Time taken by bicycle:
\[ \text{Time}_{\text{bicycle}} = \frac{y}{10} \quad \text{(3)} \]

3. **Total Time**:
The total time taken is given as 9 hours. Therefore, we can write:
\[ \frac{x}{5} + \frac{y}{10} = 9 \quad \text{(4)} \]

4. **Substituting Equation (1) into Equation (4)**:
From equation (1), we can express \( y \) in terms of \( x \):
\[ y = 50 - x \]
Substitute \( y \) into equation (4):
\[ \frac{x}{5} + \frac{50 - x}{10} = 9 \]

5. **Solve for \( x \)**:
To eliminate the fractions, multiply the entire equation by 10:
\[ 2x + (50 - x) = 90 \]
Simplifying gives:
\[ 2x + 50 - x = 90 \]
\[ x + 50 = 90 \]
\[ x = 90 - 50 \]
\[ x = 40 \]

6. **Find \( y \)**:
Now substitute \( x \) back into equation (1) to find \( y \):
\[ y = 50 - x = 50 - 40 = 10 \]

7. **Conclusion**:
The distance traveled by bicycle is:
\[ \boxed{10 \text{ km}} \]