A man covered a certain distance by a train at the speed of 40 km/hr and covers the same distance back by walking at the speed of 8km/hr. If the whole journey took 12 hours, then what is the one side distance (in km)?

Options

A. 80
B. 60
C. 90
D. 100

Answer

To solve the problem step by step, we will use the formula for time, which is given by:

\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

### Step 1: Define the Variables
Let the one side distance be \( x \) kilometers.

### Step 2: Calculate the Time Taken by Train
The speed of the train is 40 km/hr. Therefore, the time taken to cover the distance \( x \) by train is:

\[ \text{Time by train} = \frac{x}{40} \]

### Step 3: Calculate the Time Taken by Walking
The speed of walking is 8 km/hr. Therefore, the time taken to cover the same distance \( x \) by walking is:

\[ \text{Time by walking} = \frac{x}{8} \]

### Step 4: Set Up the Equation for Total Time
According to the problem, the total time for the journey (by train and walking back) is 12 hours. Thus, we can set up the equation:

\[ \frac{x}{40} + \frac{x}{8} = 12 \]

### Step 5: Find a Common Denominator
To solve the equation, we need a common denominator. The least common multiple of 40 and 8 is 40. We can rewrite the second term:

\[ \frac{x}{8} = \frac{5x}{40} \]

Now, substituting this back into the equation gives:

\[ \frac{x}{40} + \frac{5x}{40} = 12 \]

### Step 6: Combine the Terms
Now, we can combine the fractions:

\[ \frac{x + 5x}{40} = 12 \]

This simplifies to:

\[ \frac{6x}{40} = 12 \]

### Step 7: Solve for \( x \)
Now, multiply both sides by 40 to eliminate the fraction:

\[ 6x = 12 \times 40 \]

Calculating the right side:

\[ 6x = 480 \]

Now, divide both sides by 6:

\[ x = \frac{480}{6} = 80 \]

### Conclusion
Thus, the one side distance is:

\[ \boxed{80} \text{ km} \]

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