Pure ghee costing Rs.100 per kilogram and vegetable oil costing Rs.50 per kilogram are mixed in some ratio and sold at Rs.96 per kilogram so as to gain 20%. In what ratio is ghee and oil mixed?

Correct option is B

Given:

Cost of ghee per kg = Rs.100
Cost of vegetable oil per kg = Rs.50
Selling price of the mixture = Rs.96 per kg
Profit = 20%

The cost price (CP) of the mixture using the given profit percentage.

We know the selling price (SP) of the mixture is Rs.96 per kg, and the profit is 20%.

​$$CP = \frac{SP}{1 + \text{Profit\%}} \\\ \\CP = \frac{96}{1 + \frac{20}{100}} \\\ \\CP = \frac{96}{1.2} = 80 \, \text{Rs. per kg}$$​​

Let the ratio of mixing ghee and vegetable oil be x : y.
The price of the mixture can be expressed as the weighted average of the prices of ghee and oil.
Price of the mixture = $$\frac{x \times 100 + y \times 50}{x + y}$$​​

Now, we know the price of the mixture is Rs.80. So,
​$$\frac{x \times 100 + y \times 50}{x + y} = 80$$​​

Multiplying both sides by (x + y):
​$$x \times 100 + y \times 50 = 80 \times (x + y) \\\Rightarrow 100x + 50y = 80x + 80y \\\Rightarrow 100x - 80x = 80y - 50y \\\Rightarrow 20x = 30y \\\Rightarrow \frac{x}{y} = \frac{30}{20} = \frac{3}{2}$$​​

Thus, the ratio of ghee and oil is 3:2.

Alternative Method:

Ratio of Ghee and oil = 30:20 = 3:2