A taxi meter shows charges of ₹ 50 for the first two kilometres of journey and ₹ 16 for every subsequent kilometre travelled. Manju pays 258 as fare to travel from her house to the railway station. How far is the railway station from her home ?

The correct answer is 15 km (Option 3).

Step-by-step Explanation:

1. Understand the given details:
- Total fare paid by Manju = ₹ 258
- Charge for the first 2 kilometres = ₹ 50
- Rate for every subsequent kilometre = ₹ 16 per km

2. Calculate the remaining fare after paying for the first 2 km:
$\text{Remaining fare}=\text{Total fare}-\text{Charge for first 2 km}$
$\text{Remaining fare}=258-50=208$
So, the remaining fare spent on the subsequent journey is ₹ 208.

3. Calculate the distance travelled after the first 2 km:
Since each subsequent kilometre costs ₹ 16, the distance covered in the subsequent journey is:
$\text{Subsequent distance}=\frac{208}{16}$
$\text{Subsequent distance}=13\text{km}$

4. Calculate the total distance from home to the railway station:
$\text{Total distance}=\text{First 2 km}+\text{Subsequent distance}$
$\text{Total distance}=2\text{km}+13\text{km}=15\text{km}$

Therefore, the railway station is 15 km far from her home.