Question

From Dharmapuri bus stand if we buy $2$ tickets to Palacode and $3$ tickets to Karimangalam the total cost is Rs.$32,$ but if we buy $3$ tickets to Palacode and one ticket to Karimangalam the total cost is Rs. $27$. Find the fares from Dharmapuri to Palacode and to Karimangalam.

Answer 1

Let the fare from Dharmpuri to Palacode be Rs. x and to Karimangalam be Rs. y.
From the given data, we have
$2x+3y=32$ ......... (1)
$3x+y=27$ ......... (2)
Equation (2) becomes, $y=27-3x$ (3)
Substituting y in (1) we get, $2x+3(27-3x)=32$
$\Rightarrow 2x+81-9x=32$
$2x-9x=32-81$
$-7x=-49$
$\therefore x=\frac{-49}{-7}=7$
Substituting x = 7 in (3) we get, $y=27-3\left(7\right)=27-21=6$
$\therefore$ The fare from Dharmapuri to Palacode is Rs. 7 and to Karimangalam is Rs. 6.