A man covers a distance of 110 km between two cities in 10 hours. He travelled partly on foot at 9 km/hr and partly on a bicycle at 15 km/hr. Find the distance travelled on foot.

Options

A. 60 km
B. 92 km
C. 94 km
D. 96 km

Answer

To solve the problem, we need to find the distance travelled on foot by a man who covers a total distance of 110 km in 10 hours, partly on foot at a speed of 9 km/hr and partly on a bicycle at a speed of 15 km/hr.

### Step-by-Step Solution:

1. **Define Variables:**
Let \( x \) be the distance travelled on foot (in km). Therefore, the distance travelled by bicycle would be \( 110 - x \) km.

2. **Set Up Time Equations:**
The time taken to walk the distance \( x \) at a speed of 9 km/hr is given by:
\[ \text{Time on foot} = \frac{x}{9} \]
The time taken to travel the distance \( 110 - x \) at a speed of 15 km/hr is given by:
\[ \text{Time on bicycle} = \frac{110 - x}{15} \]

3. **Total Time Equation:**
Since the total time taken for the journey is 10 hours, we can set up the equation:
\[ \frac{x}{9} + \frac{110 - x}{15} = 10 \]

4. **Clear the Fractions:**
To eliminate the fractions, we can multiply the entire equation by the least common multiple of 9 and 15, which is 45:
\[ 45 \left(\frac{x}{9}\right) + 45 \left(\frac{110 - x}{15}\right) = 45 \cdot 10 \]
This simplifies to:
\[ 5x + 3(110 - x) = 450 \]

5. **Expand and Simplify:**
Expanding the equation gives:
\[ 5x + 330 - 3x = 450 \]
Combining like terms results in:
\[ 2x + 330 = 450 \]

6. **Solve for \( x \):**
Subtract 330 from both sides:
\[ 2x = 450 - 330 \]
\[ 2x = 120 \]
Now, divide by 2:
\[ x = 60 \]

7. **Conclusion:**
The distance travelled on foot is \( 60 \) km.

### Final Answer:
The distance travelled on foot is **60 km**.