In what ratio sugar of Rs. 38/kg and Rs. 30/kg be mixed so that on selling the mixture at Rs. 35.2/kg, there is a 10% profit?

Given Profit = 10%, Selling Price = Rs. 35.2

Cost Price = Selling Price/(1 + Profit%) = 35.2/(1 + 10%) = 35.2/(1 + 0.1) = 35.2/1.1 = Rs. 32

Now find the ratio in which the two varieties of sugar need to be mixed to get a cost price of Rs. 32

Using the formula for Allegations,

Quantity of lesser price/Quantity of higher price = (Average - Price of lesser quantity)/(Price of higher quantity - Average)

⇒ (32 – 30)/(38 – 32) = 2/6 = 1 : 3

∴ Required ratio = 1 : 3