A gym charges a fixed monthly fee and an additional cost per hour for using the badminton court. A student using the gym observed that when she used the badminton court for 10 hours, her bill was ₹ 800. When she used it for 15 hours, her bill was ₹ 1100. If the monthly bill $y$ depends on the hours of the use of the badminton court, $x$, according to the relation $y = ax + b$, find the values of $a$ and $b$. [Page No. 27]

Given relation is $y = ax + b$

When $x = 10$, $y$ becomes $800$, then the expression is given by

$$800 = 10a + b \tag{i}$$

When $x = 15$, $y$ becomes $1100$, then the expression is given by

$$1100 = 15a + b \quad \dots (\text{ii})$$

Subtract eq. (i) from eq. (ii); we have

$1100 - 800 = 15a + b - 10a - b$

$300 = 5a$

$\Rightarrow a = 60$

Substitute in eq. (i), we have

$b = 800 - 10(60) = 200$

Hence, the values of a and b are 60 and 200 respectively.