The taxi charges in a city consist of a fixed charge together with the charge . . .

Question :  The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is ₹ 105 and for a journey of 15 km, the charge paid is ₹ 155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of 25 km?

Doubt by Gurpreet 

Solution : 

Let the fixed charge be ₹ x
and the charge per km be ₹ y

ATQ
x+10y=105 — (1)
x+15y=155 — (2)

Using equation (1)
x+10y=105
x=105-10y — (3)
Putting in equation (2)
[105-10y]+15y=155
105-10y+15y=155
-10y+15y=155-105
5y=50
y=50/5
y=10


Putting in equation (3)

x=105-10(10)
x=105-100
x=5

Fixed charge = ₹ 5
Charge Per Km = ₹10


For a Distance of 25 km
Total Charges
= x+25y
= 5+25(10)
= 5+250
= 255
So, for a distance of 25 km, the person has to pay ₹ 255.