A man covers 3/5 of the total distance by train and the remaining 40 km by bus. What is his total journey (in km)?

Options

A. 50
B. 75
C. 100
D. 150

Answer

To solve the problem step by step, we can follow these instructions:

1. **Define the Total Distance**: Let the total distance of the journey be represented by \( x \) km.

2. **Distance Covered by Train**: According to the problem, the man covers \( \frac{3}{5} \) of the total distance by train. Therefore, the distance covered by train is:
\[ \text{Distance by train} = \frac{3}{5}x \]

3. **Distance Covered by Bus**: The remaining distance, which is covered by bus, is given as 40 km. We can express the remaining distance as:
\[ \text{Remaining distance} = x - \frac{3}{5}x \]

4. **Simplify the Remaining Distance**: To simplify the remaining distance, we can find a common denominator:
\[ x - \frac{3}{5}x = \frac{5}{5}x - \frac{3}{5}x = \frac{2}{5}x \]
So, the distance covered by bus is:
\[ \frac{2}{5}x = 40 \text{ km} \]

5. **Set Up the Equation**: Now we can set up the equation based on the distance covered by bus:
\[ \frac{2}{5}x = 40 \]

6. **Solve for \( x \)**: To find the total distance \( x \), we can multiply both sides of the equation by 5:
\[ 2x = 40 \times 5 \]
\[ 2x = 200 \]
Now, divide both sides by 2:
\[ x = \frac{200}{2} = 100 \text{ km} \]

7. **Conclusion**: The total journey is \( 100 \) km.