In what ratio should sugar costing ₹41 per kg be mixed with sugar costing ₹69 per kg so that by selling the mixture at ₹73.5 per kg, there is a profit of 50%?

Correct option is A

Given:

Cost of sugar 1 (₹41 per kg)

Cost of sugar 2 (₹69 per kg)

Selling price of the mixture = ₹73.5 per kg

Desired profit = 50%

Formula Used:

Cost price of mixture = Selling price × $$\frac{100}{100 + \text{Profit Percentage}}$$​​

Alligation:

The ratio of the quantities of sugar 1 and sugar 2 is given by:

​$$\text{Ratio} = \frac{\text{Cost of sugar 2} - \text{Cost of mixture}}{\text{Cost of mixture} - \text{Cost of sugar 1}}$$​

Solution:

Cost price of mixture = 73.5 $$\times \frac{100}{100 + 50} = 73.5 \times \frac{100}{150}$$​ = 49

Apply the alligation formula:

Ratio = $$\frac{69 - 49}{49 - 41} = \frac{20}8$$​​

Thus, the sugar costing ₹41 per kg and ₹69 per kg should be mixed in the ratio of 20 : 8.