In what ratio should sugar costing ₹17 per kg be mixed with sugar costing ₹72 per kg so that by selling the mixture at ₹41.3 per kg, there is a profit of 18%?

Correct option is C

Given:

Cost of sugar 1 (₹17 per kg)

Cost of sugar 2 (₹72 per kg)

Selling price of the mixture = ₹41.3 per kg

Desired profit = 18%

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 = 41.3 $$\times \frac{100}{100 + 18} = 41.3 \times \frac{100}{118}= 35$$​

Cost of mixture = 35 per kg

Apply the alligation formula:

Ratio =$$\frac{72 - 35}{35 - 17} = \frac{37}{18}$$​

Thus, the sugar costing ₹17 per kg and ₹72 per kg should be mixed in the ratio of 37 : 18.