Question

The total expenditure per month of a household consists of a fixed rent of the house and mess charges depending upon the number of people sharing the house. The total monthly expenditure is Rs. $3900$ for $2$ people and Rs. $7500$ for $5$ people. Find the rent of the house and the mess charges per head per month.

Answer 1

Let the monthly rent of the house be Rs x and the mess charges per head per month be Rs y.

According to the given conditions, we have,
$x+2y=3900$ (i)
$x+5y=7500$ .(ii)

Substracting equation (ii) from equation (i), we get
$-3y=-3600\Rightarrow y=1200$

Putting $y=1200$ in equation (i), we get $x=1500$

Hence, monthly rent $=$Rs. $1500$ and mess charges per head per month $=$Rs. $1200$.