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 option is 15 km.

Step 1: Understand the given information
Total fare paid by Manju = ₹ 258
Charge for the first 2 km = ₹ 50
Rate for every subsequent kilometre (after the first 2 km) = ₹ 16 per km

Step 2: Calculate the remaining amount spent on subsequent kilometres
To find out how much money was spent on the journey beyond the initial 2 km, subtract the fixed charge for the first 2 km from the total fare paid:

$\text{Remaining fare}=\text{Total fare}-\text{Fixed fare for first 2 km}$

$\text{Remaining fare}=258-50=208$

So, ₹ 208 was spent on the subsequent distance.

Step 3: Calculate the subsequent distance travelled
Since every subsequent kilometre costs ₹ 16, divide the remaining fare by the rate per kilometre:

$\text{Subsequent distance}=\frac{208}{16}=13\text{km}$

Step 4: Find the total distance from her house to the railway station
The total distance is the sum of the first 2 km and the subsequent distance travelled:

$\text{Total distance}=2\text{km}+13\text{km}=15\text{km}$

Thus, the railway station is 15 km away from Manju's home.