Rajesh goesto his office at the speed of 25 km/hr and returnsto his homeat the speed of 20 km/hr. If he takes total 9 hours, then whatis the distance between his office and home?

Options

A. 120km
B. 90km
C. 140km
D. 100km

Answer

To solve the problem step by step, we can follow this approach:

### Step 1: Define the variables
Let the distance between Rajesh's home and office be \( x \) kilometers.

### Step 2: Calculate the time taken for each journey
- Time taken to go to the office at a speed of 25 km/hr:
\[ \text{Time to office} = \frac{x}{25} \]
- Time taken to return home at a speed of 20 km/hr:
\[ \text{Time to home} = \frac{x}{20} \]

### Step 3: Set up the equation for total time
According to the problem, the total time for both journeys is 9 hours. Therefore, we can write the equation:
\[ \frac{x}{25} + \frac{x}{20} = 9 \]

### Step 4: Find a common denominator
To solve the equation, we need a common denominator for the fractions. The least common multiple of 25 and 20 is 100. We can rewrite the equation as:
\[ \frac{4x}{100} + \frac{5x}{100} = 9 \]

### Step 5: Combine the fractions
Now, combine the fractions:
\[ \frac{4x + 5x}{100} = 9 \]
This simplifies to:
\[ \frac{9x}{100} = 9 \]

### Step 6: Solve for \( x \)
To isolate \( x \), multiply both sides by 100:
\[ 9x = 900 \]
Now, divide by 9:
\[ x = 100 \]

### Conclusion
The distance between Rajesh's office and home is \( 100 \) kilometers.

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