From his home, Rahul walks `(6)/(7) km` towards school and then returns `(5)/(6) km` on the same way towards his home to reach a landmark. How far is he now from his home ?

Options

A. `(1)/(42) km `
B. `(1)/(43) km`
C. `(30)/(42) km`
D. `(11)/(42) km`

Answer

To find out how far Rahul is from his home after walking towards school and then returning, we can follow these steps:

### Step 1: Identify the distances
Rahul walks \( \frac{6}{7} \) km towards school and then returns \( \frac{5}{6} \) km towards home.

### Step 2: Assign positive and negative values
We can consider the distance towards school as positive and the distance returned as negative. Thus, we can express the total distance from home as:
\[ \text{Distance from home} = \frac{6}{7} - \frac{5}{6} \]

### Step 3: Find a common denominator
To perform the subtraction, we need a common denominator for the fractions \( \frac{6}{7} \) and \( \frac{5}{6} \). The least common multiple (LCM) of 7 and 6 is 42.

### Step 4: Convert the fractions
Now we convert both fractions to have the common denominator of 42:
\[ \frac{6}{7} = \frac{6 \times 6}{7 \times 6} = \frac{36}{42} \]
\[ \frac{5}{6} = \frac{5 \times 7}{6 \times 7} = \frac{35}{42} \]

### Step 5: Perform the subtraction
Now we can subtract the two fractions:
\[ \frac{36}{42} - \frac{35}{42} = \frac{36 - 35}{42} = \frac{1}{42} \]

### Step 6: Conclusion
Rahul is now \( \frac{1}{42} \) km away from his home.