A man travels 35km partly at 4 km/hr and at 5 km/hr if he cover former distance at 5km/hr and later distance at 4 km/hr, he could cover 2 km more in the same time the time taken to cover the whole distance at original rate is

Options

A. 9 hours
B. 7 hours
C. (4)1/2 hours
D. 8 hours

Answer

To solve the problem, we need to determine the time taken by the man to travel a total distance of 35 km at two different speeds. We will break down the distance into two parts, one part traveled at 4 km/hr and the other at 5 km/hr.

### Step-by-Step Solution:

1. **Let the distances be defined**:
- Let the distance traveled at 5 km/hr be \( x \) km.
- Therefore, the distance traveled at 4 km/hr will be \( (35 - x) \) km.

2. **Set up the time equations**:
- The time taken to travel \( x \) km at 5 km/hr is given by:
\[ \text{Time}_1 = \frac{x}{5} \]
- The time taken to travel \( (35 - x) \) km at 4 km/hr is given by:
\[ \text{Time}_2 = \frac{35 - x}{4} \]

3. **Total time for the original journey**:
- The total time taken for the journey at the original speeds is:
\[ \text{Total Time} = \frac{x}{5} + \frac{35 - x}{4} \]

4. **Consider the alternative scenario**:
- If the man travels the first part at 4 km/hr and the second part at 5 km/hr, the distances remain the same:
- The time taken to travel \( x \) km at 4 km/hr is:
\[ \text{Time}_1' = \frac{x}{4} \]
- The time taken to travel \( (35 - x) \) km at 5 km/hr is:
\[ \text{Time}_2' = \frac{35 - x}{5} \]

5. **Total time for the alternative journey**:
- The total time taken for this journey is:
\[ \text{Total Time}' = \frac{x}{4} + \frac{35 - x}{5} \]

6. **Set up the equation based on the problem statement**:
- According to the problem, in the alternative scenario, he could cover 2 km more in the same time:
\[ \text{Total Time} = \text{Total Time}' \quad \text{(for 35 km)} \quad \text{and} \quad \text{Total Time}' \quad \text{(for 37 km)} \]
- Therefore, we can set up the equation:
\[ \frac{x}{5} + \frac{35 - x}{4} = \frac{x}{4} + \frac{37 - x}{5} \]

7. **Solve the equation**:
- To solve this equation, first find a common denominator, which is 20:
\[ \frac{4x}{20} + \frac{5(35 - x)}{20} = \frac{5x}{20} + \frac{4(37 - x)}{20} \]
- Simplifying gives:
\[ 4x + 175 - 5x = 5x + 148 - 4x \]
- Rearranging terms leads to:
\[ 175 - 5x = 148 + x \]
- Solving for \( x \):
\[ 175 - 148 = 5x + x \implies 27 = 6x \implies x = \frac{27}{6} = 4.5 \text{ km} \]

8. **Find the other distance**:
- The distance traveled at 4 km/hr is:
\[ 35 - x = 35 - 4.5 = 30.5 \text{ km} \]

9. **Calculate total time at original rates**:
- Now we can calculate the total time taken at the original rates:
\[ \text{Total Time} = \frac{4.5}{5} + \frac{30.5}{4} \]
- Calculating each part:
\[ \text{Total Time} = 0.9 + 7.625 = 8.525 \text{ hours} \]

### Final Answer:
The time taken to cover the whole distance at the original rate is approximately **8.525 hours**.