Question

Three qualities of milk costing rs 3, rs 3.25 and rs 2.60 per litre are mixed and the mixture is then sold at rs. 3.54 per litre to earn a profit of 20%. In what proportion should the three qualities of milk be mixed?

Answer 1

Answer:

Let the 3 types of milk be “A”, “B” & “C” whose C.P. per litre is Rs.3, Rs.3.25 and Rs.2.60 respectively.

S.P. of the mixture of the three milk = Rs. 3.54 per litre

Profit% = 20%

∴ Cost of the mixture

= [100/(100+P%)] * S.P.

= [100 * 3.54]/[100+20]

= Rs. 2.95 per litre

Now, to find the ratio of A, B & C in the mixture, we will use the method of alligation :

A / C = [2.95-2.60] / [3-2.95] = 0.35 / 0.05 = 35 / 5 = 7 / 1

And,

B / C = [2.95-2.60] / [3.25-2.95] = 0.35 / 0.30 = 35 / 30 = 7 / 6

So, we have

A : C = 7 : 1 and B : C = 7 : 6

∴ A :  B : C = (7*6) : (7*1) : (6*1) = 42 : 7 : 6

Thus, the three qualities of the milk should be mixed in the proportion of 42:7:6.