If a person had walked at the speed of 15 km/h instead of 10 km/h, he would have walked 25 km more. The actual distance travelled by him was:

Options

A. 75 km
B. 56 km
C. 50 km
D. 80 km

Answer

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

### Step 1: Understand the problem
We know that if a person walks at 15 km/h instead of 10 km/h, he would cover 25 km more distance. We need to find the actual distance he traveled.

### Step 2: Define the variables
Let the time taken to travel the actual distance be \( x \) hours.

### Step 3: Calculate the distances
- Distance traveled at 10 km/h: \( \text{Distance}_1 = 10 \times x \)
- Distance traveled at 15 km/h: \( \text{Distance}_2 = 15 \times x \)

### Step 4: Set up the equation
According to the problem, the difference in distance when walking at 15 km/h instead of 10 km/h is 25 km. Therefore, we can set up the equation:
\[ \text{Distance}_2 - \text{Distance}_1 = 25 \]
Substituting the expressions for Distance_1 and Distance_2:
\[ 15x - 10x = 25 \]

### Step 5: Simplify the equation
This simplifies to:
\[ 5x = 25 \]

### Step 6: Solve for \( x \)
Dividing both sides by 5 gives:
\[ x = 5 \]
So, the time taken to travel the actual distance is 5 hours.

### Step 7: Calculate the actual distance
Now that we have the time, we can find the actual distance traveled using the speed of 10 km/h:
\[ \text{Actual Distance} = \text{Speed} \times \text{Time} = 10 \times 5 = 50 \text{ km} \]

### Final Answer
The actual distance traveled by him was **50 km**.

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