A man covers `(2)/(15)` of the total journey by train, `(9)/(20)` by bus and the remaining 10km on foot. His total journey (in km) is

Options

A. `15.6`
B. 24
C. `16.4`
D. `12.8`

Answer

To solve the problem step by step, we will denote the total journey distance as \( x \) kilometers.

### Step 1: Set up the equation based on the journey segments
The man covers:
- \( \frac{2}{15} \) of the total journey by train
- \( \frac{9}{20} \) of the total journey by bus
- The remaining distance on foot is 10 km

We can express the total journey as:
\[ \frac{2}{15}x + \frac{9}{20}x + 10 = x \]

### Step 2: Find a common denominator
To solve the equation, we need to combine the fractions. The least common multiple (LCM) of 15 and 20 is 60. We will convert each fraction to have a denominator of 60:
- \( \frac{2}{15} = \frac{2 \times 4}{15 \times 4} = \frac{8}{60} \)
- \( \frac{9}{20} = \frac{9 \times 3}{20 \times 3} = \frac{27}{60} \)

Now we can rewrite the equation:
\[ \frac{8}{60}x + \frac{27}{60}x + 10 = x \]

### Step 3: Combine the fractions
Combine the fractions on the left side:
\[ \frac{8x + 27x}{60} + 10 = x \]
This simplifies to:
\[ \frac{35}{60}x + 10 = x \]

### Step 4: Isolate \( x \)
To isolate \( x \), we will move \( \frac{35}{60}x \) to the right side:
\[ 10 = x - \frac{35}{60}x \]
This can be rewritten as:
\[ 10 = \left(1 - \frac{35}{60}\right)x \]
Calculating \( 1 - \frac{35}{60} \):
\[ 1 = \frac{60}{60} \quad \Rightarrow \quad 1 - \frac{35}{60} = \frac{60 - 35}{60} = \frac{25}{60} \]
Thus, we have:
\[ 10 = \frac{25}{60}x \]

### Step 5: Solve for \( x \)
Now, we can solve for \( x \) by multiplying both sides by \( \frac{60}{25} \):
\[ x = 10 \times \frac{60}{25} \]
Calculating the right side:
\[ x = \frac{600}{25} = 24 \]

### Conclusion
The total journey is \( x = 24 \) kilometers.