A man travels `2/15` of the total journey by rail,`9/20` by car and the remaining 10 km on foot. His total journey in km is

Options

A. 36
B. 40
C. 30
D. 24

Answer

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

### Step 1: Define the total journey
Let the total journey be represented as \( x \) km.

### Step 2: Calculate the distance traveled by rail
The distance traveled by rail is given as \( \frac{2}{15} \) of the total journey:
\[ \text{Distance by rail} = \frac{2}{15} \times x \]

### Step 3: Calculate the distance traveled by car
The distance traveled by car is given as \( \frac{9}{20} \) of the total journey:
\[ \text{Distance by car} = \frac{9}{20} \times x \]

### Step 4: Calculate the remaining distance
The remaining distance is traveled on foot, which is given as 10 km. Therefore, we can express the remaining distance as:
\[ \text{Remaining distance} = x - \left(\frac{2}{15}x + \frac{9}{20}x\right) \]

### Step 5: Set up the equation
Since the remaining distance is equal to 10 km, we can set up the equation:
\[ x - \left(\frac{2}{15}x + \frac{9}{20}x\right) = 10 \]

### Step 6: Find a common denominator
To simplify the equation, we need a common denominator for the fractions. The least common multiple (LCM) of 15 and 20 is 60. We can rewrite the fractions:
\[ \frac{2}{15} = \frac{8}{60}, \quad \frac{9}{20} = \frac{27}{60} \]
Thus, the equation becomes:
\[ x - \left(\frac{8}{60}x + \frac{27}{60}x\right) = 10 \]

### Step 7: Combine the fractions
Combine the fractions on the left side:
\[ x - \frac{35}{60}x = 10 \]

### Step 8: Simplify the equation
This simplifies to:
\[ \frac{25}{60}x = 10 \]

### Step 9: Solve for \( x \)
To find \( x \), multiply both sides by \( \frac{60}{25} \):
\[ x = 10 \times \frac{60}{25} \]
Calculating this gives:
\[ x = 10 \times 2.4 = 24 \text{ km} \]

### Conclusion
The total journey is \( 24 \) km.