Question

Two varieties of oil are mixed in the ratio 4:3 to produce first quality and if they are mixed in the ratio 2:3 second quality is obtained. how many kg. of the first quality be mixed with 10kg of the second quality so that a third quality having the two verieties in the ratio 5 : 4 may be produced

Answer 1

Let the common ration of the first quality oil be x. The ratio is 4:3
Therefore, the total quantity of the first quality oil=4x+3x=7x

 The total quantity of the second quality oil = 10kg
 The ratio is 2:3
Therefore, the quantity of first oil variety = (2/5)*10 = 4kg
                   The quantity of second oil variety = (3/5) * 10 = 6 kg
 The third ratio is got by mixing the first quality and 10 kg of second quality.

  Therefore, (4x+4)/(3x+6) = 5/4
 4*(4x+4) = 5*(3x+6)
16x+16 = 15x+30
Grouping like terms together,
16x-15x=30-16
x=14
The total quantity of first quality oil = 7x kg
                                                        = 7 * 14 kg
                                                         =98 kg