From a starting point A, Rahul walks 3/4 km towards east and then 6/7 km towards west to reach point C.
How much total distance Rahul walks to reach point C ?

Options

A. `(45)/(28) km`
B. `(43)/(28) km`
C. `(47)/(28) km`
D. `(49)/(28) km`

Answer

To find the total distance Rahul walks to reach point C, we need to add the distances he walked in both directions.

### Step-by-Step Solution:

1. **Identify the distances walked**:
- Rahul walks \( \frac{3}{4} \) km towards the east.
- Then, he walks \( \frac{6}{7} \) km towards the west.

2. **Calculate the total distance**:
- The total distance Rahul walks is the sum of the distances he walked towards the east and west:
\[ \text{Total Distance} = \frac{3}{4} + \frac{6}{7} \]

3. **Find a common denominator**:
- The denominators are 4 and 7. The least common multiple (LCM) of 4 and 7 is 28.
- Convert \( \frac{3}{4} \) to a fraction with a denominator of 28:
\[ \frac{3}{4} = \frac{3 \times 7}{4 \times 7} = \frac{21}{28} \]
- Convert \( \frac{6}{7} \) to a fraction with a denominator of 28:
\[ \frac{6}{7} = \frac{6 \times 4}{7 \times 4} = \frac{24}{28} \]

4. **Add the fractions**:
- Now, add the two fractions:
\[ \frac{21}{28} + \frac{24}{28} = \frac{21 + 24}{28} = \frac{45}{28} \]

5. **Final Result**:
- The total distance Rahul walks to reach point C is:
\[ \frac{45}{28} \text{ km} \]