A man performs `4/15` of the total journey by rail, `9/20` by bus and the remaining 5 km by walking. His total journey is

Options

A. (a) 16 km
B. (b) 17.647 km
C. (c) 17.476 km
D. (d) 17.764 km

Answer

To find the total journey of the man, we can denote the total distance of the journey as \( x \) km.

1. **Calculate the distance traveled by rail:**
The man travels \( \frac{4}{15} \) of the total journey by rail. Therefore, the distance traveled by rail is:
\[ \text{Distance by rail} = \frac{4}{15} x \]

2. **Calculate the distance traveled by bus:**
The man travels \( \frac{9}{20} \) of the total journey by bus. Therefore, the distance traveled by bus is:
\[ \text{Distance by bus} = \frac{9}{20} x \]

3. **Calculate the total distance traveled by rail and bus:**
To find the total distance traveled by rail and bus, we add the two distances:
\[ \text{Total distance by rail and bus} = \frac{4}{15} x + \frac{9}{20} x \]

4. **Find a common denominator:**
The least common multiple (LCM) of 15 and 20 is 60. We will convert the fractions to have a common denominator:
\[ \frac{4}{15} = \frac{16}{60}, \quad \frac{9}{20} = \frac{27}{60} \]
Therefore,
\[ \text{Total distance by rail and bus} = \frac{16}{60} x + \frac{27}{60} x = \frac{43}{60} x \]

5. **Calculate the remaining distance:**
The remaining distance that the man walks is given as 5 km. Thus, we can write:
\[ \text{Remaining distance} = x - \left(\frac{43}{60} x\right) = 5 \]

6. **Set up the equation:**
Now we can set up the equation:
\[ x - \frac{43}{60} x = 5 \]
This simplifies to:
\[ \frac{17}{60} x = 5 \]

7. **Solve for \( x \):**
To find \( x \), we multiply both sides by \( \frac{60}{17} \):
\[ x = 5 \times \frac{60}{17} = \frac{300}{17} \approx 17.647 \]

8. **Conclusion:**
The total journey \( x \) is approximately \( 17.647 \) km.