A man performs 2/25 of his total journey by bus, 21/50 by car and the reamining 2 km on foot . Find the total journey.

Options

A. 2.5 km
B. 2.7 km
C. 3.4 km
D. 3.8 km

Answer

To find the total journey of the man, we can follow these steps:

1. **Define the total journey**: Let the total journey be represented as \( D \) km.

2. **Calculate the distance traveled by bus**: The man travels \( \frac{2}{25} \) of his total journey by bus. Therefore, the distance traveled by bus is:
\[ \text{Distance by bus} = \frac{2}{25} D \]

3. **Calculate the distance traveled by car**: The man travels \( \frac{21}{50} \) of his total journey by car. Therefore, the distance traveled by car is:
\[ \text{Distance by car} = \frac{21}{50} D \]

4. **Distance traveled on foot**: The man travels 2 km on foot.

5. **Set up the equation**: The total journey can be expressed as the sum of the distances traveled by bus, car, and on foot:
\[ D = \frac{2}{25} D + \frac{21}{50} D + 2 \]

6. **Find a common denominator**: The denominators are 25 and 50. The least common multiple (LCM) of 25 and 50 is 50. We can rewrite \( \frac{2}{25} D \) as \( \frac{4}{50} D \):
\[ D = \frac{4}{50} D + \frac{21}{50} D + 2 \]

7. **Combine the fractions**: Now, combine the fractions on the right side:
\[ D = \left(\frac{4 + 21}{50}\right) D + 2 \]
\[ D = \frac{25}{50} D + 2 \]

8. **Simplify the equation**: Since \( \frac{25}{50} = \frac{1}{2} \), we can rewrite the equation as:
\[ D = \frac{1}{2} D + 2 \]

9. **Isolate \( D \)**: To isolate \( D \), subtract \( \frac{1}{2} D \) from both sides:
\[ D - \frac{1}{2} D = 2 \]
\[ \frac{1}{2} D = 2 \]

10. **Solve for \( D \)**: Multiply both sides by 2 to find \( D \):
\[ D = 4 \text{ km} \]

Thus, the total journey is **4 km**.