Question: In a city, the taxi charges consists of two types of a charges: a fixed charge together with the charge for the distance covered. If a person travels 10km, he pays Rs 180 and for travelling 12km, he pays Rs 210. Find the fixed charges and the rate of charge per km.

Solution:

Let the fixed charge of the taxi in that city be Rs x. And, the charge per km be Rs y.

According to the question,

Condition I,
A person travels 10km and he pays Rs 180.
$or, x + 10y = 180$
$or, x = 180 - 10y$ - (i)

Condition II,
When he travels 12km, he pays Rs 210.
$or, x + 12y = 210$ - (ii)

Put the value of x from equation (i) in equation (ii), we get,

$or, 180 - 10y +12y = 210$
$or, 2y = 210 -180$
$or, 2y = 30$
$or, 2×y = 2×15$
$\therefore y = 15$

And,

Put the value of y in equation (i), we get,
$or, x = 180 - 10×15$
$or, x = 180 - 150$
$\therefore x = 30$

So, (x,y) = (30,15)

Hence, the required fixed charge of taxi in that city is Rs 30 and the rate of charge per km is Rs 15.