In what ratio should sugar costing ₹10 per kg be mixed with sugar costing ₹61 per kg so that by selling the mixture at ₹31.5 per kg, there is a profit of 26%?

Given:

Sugar costing ₹10/kg and ₹61/kg are mixed. Selling price of the mixture = ₹31.5/kg. Profit = 26%

Formula used:

Profit = Selling Price - Cost Price

Cost Price of the mixture = Selling Price / (1 + Profit%)

Alligation rule: Ratio = (Higher cost - Mean cost) : (Mean cost - Lower cost)

Calculation:

Cost Price of the mixture = ₹31.5 / (1 + 26/100)

⇒ Cost Price = ₹31.5 / (1.26)

⇒ Cost Price = ₹25

Using Alligation Rule:

 ₹10 per kg                        ₹61 per kg

                        ₹25 per kg  

      (61 - 25)             :            (25 - 10)

⇒        36                  :             15

⇒ Ratio = 36 : 15

∴ The correct answer is option (3).