If a person walks at 12km/hr instead of 10km/hr, he would have walked 1km more in the same time. What is the actual distance (in kms) travelled by him at 10k/hr in the same time?

Options

A. 8
B. 10
C. 5
D. 12

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the given information
We know that:
- The person walks at a speed of 10 km/hr.
- If he walks at a speed of 12 km/hr instead, he would cover 1 km more in the same time.

### Step 2: Set up the relationship between distance, speed, and time
Let the time taken to walk at both speeds be \( t \) hours.

Using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]

At 10 km/hr, the distance covered is:
\[ \text{Distance at 10 km/hr} = 10t \]

At 12 km/hr, the distance covered is:
\[ \text{Distance at 12 km/hr} = 12t \]

### Step 3: Set up the equation based on the information given
According to the problem, if he walks at 12 km/hr, he covers 1 km more than at 10 km/hr. Therefore, we can set up the equation:
\[ 12t = 10t + 1 \]

### Step 4: Solve the equation for \( t \)
Subtract \( 10t \) from both sides:
\[ 12t - 10t = 1 \]
\[ 2t = 1 \]

Now, divide both sides by 2:
\[ t = \frac{1}{2} \text{ hours} \]

### Step 5: Calculate the actual distance traveled at 10 km/hr
Now that we have the time, we can find the distance traveled at 10 km/hr:
\[ \text{Distance} = 10t = 10 \times \frac{1}{2} = 5 \text{ km} \]

### Final Answer
The actual distance traveled by him at 10 km/hr in the same time is **5 km**.

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