The total expenditure per month of a household consists of a fixed ren

1.	The total expenditure per month of a household consists of a fixed rent of the house and the mess charges, depending upon the number of people sharing the house. The total monthly expenditure is Rs. 3,900 for 2 people and Rs. 7,500 for 5 people. Find the rent of the house and the mess charges per head per month.
Answer» 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.

The total expenditure per month of a household consists of a fixed rent of the house and the mess charges, depending upon the number of people sharing the house. The total monthly expenditure is Rs. 3,900 for 2 people and Rs. 7,500 for 5 people. Find the rent of the house and the mess charges per head per month.

Answer»

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.