Pooja walks `4/5` km towards office from her home and then returns `2/3` km on the same way towards her home to reach a landmark. How far will she be now from her home?

Options

A. `1/15` km
B. `1/5`km
C. `2/15`km
D. `2/17`km

Answer

To find out how far Pooja is from her home after walking towards her office and then returning partway, we can follow these steps:

### Step 1: Determine the distance Pooja walked towards the office
Pooja walks \( \frac{4}{5} \) km towards her office from her home.

### Step 2: Determine the distance Pooja walked back towards home
Pooja then returns \( \frac{2}{3} \) km towards her home.

### Step 3: Calculate the distance from her home to the landmark
To find out how far Pooja is from her home after returning, we need to subtract the distance she walked back from the distance she initially walked towards the office.

So, we need to calculate:
\[ \text{Distance from home to landmark} = \text{Distance to office} - \text{Distance back} \]
This can be expressed as:
\[ \text{Distance from home to landmark} = \frac{4}{5} - \frac{2}{3} \]

### Step 4: Find a common denominator
The denominators are 5 and 3. The least common multiple (LCM) of 5 and 3 is 15. We will convert both fractions to have a denominator of 15.

- For \( \frac{4}{5} \):
\[ \frac{4}{5} = \frac{4 \times 3}{5 \times 3} = \frac{12}{15} \]

- For \( \frac{2}{3} \):
\[ \frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15} \]

### Step 5: Subtract the fractions
Now we can subtract the two fractions:
\[ \frac{12}{15} - \frac{10}{15} = \frac{12 - 10}{15} = \frac{2}{15} \]

### Conclusion
Thus, Pooja is \( \frac{2}{15} \) km away from her home.