A person goes to his office at 1/3rd of the speed at which he returns from his office if the average speed during the whole trip(i.e, one round)is 12 km/h.What is the speed of the person while he was going to his office?

Options

A. 10
B. 6
C. 8
D. can't be determined

Answer

To solve the problem, we need to find the speed of the person while going to his office, given that he travels at 1/3 of the speed when returning. The average speed for the entire trip is given as 12 km/h.

### Step-by-Step Solution:

1. **Define the Speeds**:
- Let the speed of the person while returning from the office be \( 3x \) km/h.
- Therefore, the speed while going to the office will be \( x \) km/h (since it is 1/3 of the returning speed).

2. **Distance Calculation**:
- Let the distance to the office be \( d \) km. The time taken to go to the office is \( \frac{d}{x} \) hours, and the time taken to return is \( \frac{d}{3x} \) hours.

3. **Total Time for the Round Trip**:
- The total time for the round trip is the sum of the time taken to go and return:
\[ \text{Total Time} = \frac{d}{x} + \frac{d}{3x} \]
- To combine these fractions, find a common denominator:
\[ \text{Total Time} = \frac{3d}{3x} + \frac{d}{3x} = \frac{4d}{3x} \]

4. **Average Speed Formula**:
- The average speed for the entire trip is given by the formula:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]
- The total distance for the round trip is \( 2d \):
\[ \text{Average Speed} = \frac{2d}{\frac{4d}{3x}} = \frac{2d \cdot 3x}{4d} = \frac{6x}{4} = \frac{3x}{2} \]

5. **Set Up the Equation**:
- We know the average speed is 12 km/h, so we can set up the equation:
\[ \frac{3x}{2} = 12 \]

6. **Solve for \( x \)**:
- Multiply both sides by 2:
\[ 3x = 24 \]
- Divide by 3:
\[ x = 8 \text{ km/h} \]

7. **Conclusion**:
- The speed of the person while going to his office is \( 8 \) km/h.