A person travelled `(5)/(8)`th of the distance by train `(1)/(4)` th by bus and the remaining 15 km by boat. What was the total distance travelled by him ?

Answer

To find the total distance traveled by the person, we can follow these steps:

### Step 1: Define the total distance
Let the total distance traveled by the person be denoted as \( d \).

### Step 2: Express the parts of the journey
According to the problem:
- The distance traveled by train is \( \frac{5}{8}d \).
- The distance traveled by bus is \( \frac{1}{4}d \).
- The remaining distance traveled by boat is given as 15 km.

### Step 3: Set up the equation
The sum of the distances traveled by train, bus, and boat should equal the total distance \( d \):
\[ \frac{5}{8}d + \frac{1}{4}d + 15 = d \]

### Step 4: Convert all fractions to a common denominator
To combine the fractions, we can convert \( \frac{1}{4} \) to have a denominator of 8:
\[ \frac{1}{4} = \frac{2}{8} \]
Now, substitute this back into the equation:
\[ \frac{5}{8}d + \frac{2}{8}d + 15 = d \]

### Step 5: Combine the fractions
Combine the fractions on the left side:
\[ \frac{5 + 2}{8}d + 15 = d \]
This simplifies to:
\[ \frac{7}{8}d + 15 = d \]

### Step 6: Isolate \( d \)
To isolate \( d \), subtract \( \frac{7}{8}d \) from both sides:
\[ 15 = d - \frac{7}{8}d \]
This simplifies to:
\[ 15 = \frac{1}{8}d \]

### Step 7: Solve for \( d \)
Multiply both sides by 8 to solve for \( d \):
\[ d = 15 \times 8 \]
\[ d = 120 \]

### Conclusion
The total distance traveled by the person is **120 km**.

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