Aptitude Day 105

Ratio and Proportion:

Answer of Day 104:  3:1

Problems:

1. The electricity bill of a certain establishment is partly fixed and partly varies as the number of units of electricity is consumed. When in a certain month 300 units are consumed, the bill is 2000. In another month 520 units are consumed and the bill is 3100. In yet another month 200 units are consumed. The bill for that month would be:

Solution:
             Let the fixed amount be x and the cost of each unit be y.

             300y+x = 2000    ---- Equation 1
             520y+x = 3100    ---- Equation 2
   
            By solving these 2 equations, we get
                     y = 5 and x = 500.

           The bill for the asked month is 200y+x = 200(5)+500
                                                                          = 1500.

2. The ratio of the incomes of A and B is 3:5 and the ratio of their expenditures is 2:3. If at the end of the year, A saves 300 and B saves 600, then the income of B is:

Solution:
              Their incomes are 3x and 5x respectively.
              Their expenditures are 2y and 3y respectively.

              3x-2y = 300 ----- Equation 1
              5x-3y = 600 ----- Equation 2

              By solving these 2 equations, we get
                        y = 300, x = 300.

              Income of B is 5x = 5(300)
                                            = 1500.