If a man travels at 30 km/h, he reaches his destination late by 10 minutes but if he travels at 42 km/h then he reaches 10 minutes earlier. The distance travelled by him is

Options

A. 30 km
B. 35 km
C. 45 km
D. 36 km

Answer

To solve the problem, we need to find the distance traveled by the man based on his speeds and the time differences given.

### Step-by-Step Solution:

1. **Identify the speeds and time differences**:
- Speed 1 (S1) = 30 km/h (late by 10 minutes)
- Speed 2 (S2) = 42 km/h (early by 10 minutes)
- The total time difference between the two scenarios = 10 minutes (late) + 10 minutes (early) = 20 minutes.

2. **Convert the time difference into hours**:
- 20 minutes = 20/60 hours = 1/3 hours.

3. **Use the formula for distance**:
The formula to calculate distance when given two speeds and the time difference is:
\[ \text{Distance} = \frac{S1 \times S2}{S2 - S1} \times \text{Time Difference} \]
Here, S1 = 30 km/h and S2 = 42 km/h.

4. **Substituting the values into the formula**:
\[ \text{Distance} = \frac{30 \times 42}{42 - 30} \times \frac{1}{3} \]

5. **Calculate the denominator**:
- \(42 - 30 = 12\).

6. **Calculate the numerator**:
- \(30 \times 42 = 1260\).

7. **Putting it all together**:
\[ \text{Distance} = \frac{1260}{12} \times \frac{1}{3} \]

8. **Simplifying the fraction**:
- \(\frac{1260}{12} = 105\).
- Now, multiply by \(\frac{1}{3}\):
\[ \text{Distance} = 105 \times \frac{1}{3} = 35 \text{ km}. \]

### Final Answer:
The distance traveled by him is **35 km**.