A man can cover a certain distance in 6 hours if he walks at the rate of 8 km/hr. If he covers the same distance on cycle at the rate of 12 km/hr, then what is the time (in hours) taken by him?

Options

A. 3
B. 4
C. 2
D. 5

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Calculate the Distance
We know that distance is calculated using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]

Given:
- Speed while walking = 8 km/hr
- Time taken while walking = 6 hours

Using the formula:
\[ \text{Distance} = 8 \, \text{km/hr} \times 6 \, \text{hours} \]
\[ \text{Distance} = 48 \, \text{km} \]

### Step 2: Calculate the Time Taken on Cycle
Now, we need to find out how long it takes to cover the same distance on a cycle.

Given:
- Speed while cycling = 12 km/hr
- Distance = 48 km (calculated in Step 1)

Using the formula for time:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
\[ \text{Time} = \frac{48 \, \text{km}}{12 \, \text{km/hr}} \]
\[ \text{Time} = 4 \, \text{hours} \]

### Final Answer
The time taken by him to cover the same distance on a cycle is **4 hours**.

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