Speed of Karan is 40 km/h and speed of Arjun is 60km/h. What is the ratio of time taken by each to cover the same distance?

Answer

To solve the problem of finding the ratio of the time taken by Karan and Arjun to cover the same distance, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Speeds**:
- Speed of Karan = 40 km/h
- Speed of Arjun = 60 km/h

2. **Assume a Distance**:
- Let the distance they both travel be \( x \) km.

3. **Calculate Time Taken by Karan**:
- Time is calculated using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
- For Karan:
\[ \text{Time taken by Karan} = \frac{x}{40} \text{ hours} \]

4. **Calculate Time Taken by Arjun**:
- For Arjun:
\[ \text{Time taken by Arjun} = \frac{x}{60} \text{ hours} \]

5. **Set Up the Ratio of Time Taken**:
- The ratio of the time taken by Karan to the time taken by Arjun is:
\[ \text{Ratio} = \frac{\text{Time taken by Karan}}{\text{Time taken by Arjun}} = \frac{\frac{x}{40}}{\frac{x}{60}} \]

6. **Simplify the Ratio**:
- The \( x \) in the numerator and denominator cancels out:
\[ \text{Ratio} = \frac{1/40}{1/60} = \frac{60}{40} \]
- Simplifying \( \frac{60}{40} \) gives:
\[ \text{Ratio} = \frac{3}{2} \]

7. **Final Answer**:
- The ratio of the time taken by Karan to the time taken by Arjun is \( 3:2 \).