Anil goes to his office at the speed of 35 km/hr and returns to his home at the speed of 30 km/hr. If he takes total 39 hours, then what is the distance between his office and home?

Options

A. a) 420 km
B. b) 525 km
C. c) 630 km
D. d) 210 km

Answer

To solve the problem, we need to find the distance between Anil's office and home based on the speeds at which he travels and the total time taken for the round trip.

### Step-by-Step Solution:

1. **Define Variables:**
Let the distance between Anil's office and home be \( x \) km.

2. **Calculate Time Taken for Each Trip:**
- Time taken to go to the office at 35 km/hr:
\[ T_1 = \frac{x}{35} \]
- Time taken to return home at 30 km/hr:
\[ T_2 = \frac{x}{30} \]

3. **Set Up the Equation:**
The total time for the round trip is given as 39 hours. Therefore, we can write the equation:
\[ T_1 + T_2 = 39 \]
Substituting the expressions for \( T_1 \) and \( T_2 \):
\[ \frac{x}{35} + \frac{x}{30} = 39 \]

4. **Find a Common Denominator:**
The least common multiple of 35 and 30 is 210. We will multiply each term by 210 to eliminate the fractions:
\[ 210 \left(\frac{x}{35}\right) + 210 \left(\frac{x}{30}\right) = 210 \cdot 39 \]
Simplifying each term:
\[ 6x + 7x = 8190 \]

5. **Combine Like Terms:**
Combine \( 6x \) and \( 7x \):
\[ 13x = 8190 \]

6. **Solve for \( x \):**
Divide both sides by 13:
\[ x = \frac{8190}{13} = 630 \]

7. **Conclusion:**
The distance between Anil's office and home is \( 630 \) km.