A man travelled a distance of 61 km in 9 hours, parts on foot at the rate of 4km/hr and partly on bicycle at the rate of 9km/hr. The distance travelled on foot was

Options

A. 12km
B. 16km
C. 20km
D. 24km

Answer

To solve the problem step by step, we will use the information provided in the question regarding the distances traveled on foot and by bicycle, as well as their respective speeds.

### Step-by-Step Solution:

1. **Define Variables:**
Let \( x \) be the distance traveled on foot (in km).
Therefore, the distance traveled on the bicycle will be \( 61 - x \) km.

2. **Write the Speeds:**
The speed on foot is given as \( 4 \) km/hr, and the speed on the bicycle is \( 9 \) km/hr.

3. **Calculate Time Taken:**
The time taken to travel on foot can be calculated using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
Thus, the time taken on foot is:
\[ \text{Time on foot} = \frac{x}{4} \]
The time taken on the bicycle is:
\[ \text{Time on bicycle} = \frac{61 - x}{9} \]

4. **Set Up the Equation:**
According to the problem, the total time taken for the journey is \( 9 \) hours. Therefore, we can set up the equation:
\[ \frac{x}{4} + \frac{61 - x}{9} = 9 \]

5. **Clear the Fractions:**
To eliminate the fractions, we can multiply the entire equation by the least common multiple (LCM) of \( 4 \) and \( 9 \), which is \( 36 \):
\[ 36 \left(\frac{x}{4}\right) + 36 \left(\frac{61 - x}{9}\right) = 36 \cdot 9 \]
This simplifies to:
\[ 9x + 4(61 - x) = 324 \]

6. **Distribute and Combine Like Terms:**
Expanding the equation gives:
\[ 9x + 244 - 4x = 324 \]
Combining like terms results in:
\[ 5x + 244 = 324 \]

7. **Isolate \( x \):**
Subtract \( 244 \) from both sides:
\[ 5x = 324 - 244 \]
Simplifying gives:
\[ 5x = 80 \]

8. **Solve for \( x \):**
Divide both sides by \( 5 \):
\[ x = \frac{80}{5} = 16 \]

9. **Conclusion:**
The distance traveled on foot is \( 16 \) km.

### Final Answer:
The distance traveled on foot is **16 km**.