Question

The total expenditure per month of a household consist 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 1

Monthly  expenditure of two people = rent + 2 * mess charges = Rs 3900
Monthly expenditure for 5 people = rent + 5 * mess charges = Rs 7500

Subtract first equation from the second..

(  5-2) = 3 people's mess charges = Rs 7500 - 3900 = Rs  3,600 
  one persons mess charges = 3600/3 = Rs 1,200


Monthly expenditure for two people =  rent + 2 * 1200 = Rs 3900
                 rent = Rs 3900 - 2400
                 rent = Rs 1,500 

Answer 2

Answer:The rent of house is 1500/-

The mess charge per head is 7500/-

Step-by-step explanation:

Let the rent of house be; X

Let the mess charge per head be; Y

ATQ;

The first eq. is ;

X+2Y=3900 ...…...............(1)

The second eq. is ;

X+5Y=7500 ....................(2)

By calculating the both equation (by elimination method)

We get Y=1200

Now placing the value of Y in eq (1)

We get;

X + 2(1200) = 3900

X + 2400 = 3900

X = 3900 - 2400

X = 1500

Therefore;

The rent of house is 1500/-

The mess charge per person is rupees 1200/-

Hope it helps!!