Let fixed rent of the house = Rs. x
And the mess charges per head per month = Rs. y
According to the question,
x + 2y = 3900 …(i)
and x + 5y = 7500 …(ii)
On subtracting Eq. (i) from Eq. (ii), we get
x + 5y – x – 2y = 7500 – 3900
⇒ 3y = 3600
⇒ y = 1200
On putting the value of y = 1200 in Eq. (i), we get
x + 2 (1200) = 3900
⇒ x + 2400 = 3900
⇒ x = 1500
Hence, fixed rent of the house is Rs. 1500 and the mess charges per head per month is Rs. 1200.