Question

In what ratio should a variety of rice costing rs. 6 per kg be mixed with another variety of rice costing rs. 8.75 per kg to obtain a mixture costing rs. 7.50 per kg?

Answer 1

Let

Amount of Variety 1 = x Kg

Amount of Variety 2 = y Kg

Then according to given condition

   6x + 8.75y = 7.50 ............(i)

Also

x + y = 1    ( The total of Both varieties must be equal to 1 Kg )

   y = 1 - x     ............(ii) , putting this in (i) , we get

6x + 8.75( 1 - x ) = 7.50

6x + 8.75 - 8.75 x = 7. 50

6 x - 8.75 x = 7.50 - 8.75

  - 2.75 x = - 1.25

    2.75 x = 1.25

            x = 1.25/2.75

            x = 0.4545 , Putting this in (ii) , we get

 y = 1 - x = 1 - 0.4545

             y = 0.5455

So required Ratio is                

                                x     :    y

                         0.4545  :    0.5455

  Dividing both by 0.4545 , we get

                                 1      :   1.2

Multiplying both by 5 , we get

                                    5    :      6

So the required Ratio is 5 : 6