From a starting point A, Rahul walks 3/4 km towards east and then 6/7 km towards west to reach point C.
Where will he be noe from the starting point A ?

Options

A. `9//28` km towards west
B. `3//28` km towards west
C. `3//28` km towards east
D. `9//28` km towards east

Answer

To solve the problem step by step, we will analyze Rahul's movements and calculate his final position relative to the starting point A.

### Step 1: Understand the movements
Rahul first walks \( \frac{3}{4} \) km towards the east and then \( \frac{6}{7} \) km towards the west.

### Step 2: Assign directions
- East is considered positive, so walking towards the east will be a positive distance.
- West is considered negative, so walking towards the west will be a negative distance.

### Step 3: Calculate the total distance moved
- Distance towards east: \( +\frac{3}{4} \) km
- Distance towards west: \( -\frac{6}{7} \) km

### Step 4: Combine the distances
To find the net distance from point A, we need to add these two distances:
\[ \text{Net distance} = \frac{3}{4} - \frac{6}{7} \]

### Step 5: Find a common denominator
The denominators are 4 and 7. The least common multiple (LCM) of 4 and 7 is 28. We will convert both fractions to have this common denominator.

- Convert \( \frac{3}{4} \):
\[ \frac{3}{4} = \frac{3 \times 7}{4 \times 7} = \frac{21}{28} \]

- Convert \( \frac{6}{7} \):
\[ \frac{6}{7} = \frac{6 \times 4}{7 \times 4} = \frac{24}{28} \]

### Step 6: Subtract the fractions
Now we can subtract the two fractions:
\[ \text{Net distance} = \frac{21}{28} - \frac{24}{28} = \frac{21 - 24}{28} = \frac{-3}{28} \]

### Step 7: Interpret the result
The negative sign indicates that Rahul is \( \frac{3}{28} \) km towards the west from the starting point A.

### Final Answer
Rahul is \( \frac{3}{28} \) km towards the west from point A.

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