In what ratio should sugar costing ₹74 per kg be mixed with sugar costing ₹41 per kg sothat by selling the mixture at ₹85.8 per kg, there is a profit of 30%?

Correct option is C

Given:​

Cost of sugar 1 = ₹74 per kg

Cost of sugar 2 = ₹41 per kg

Selling price of the mixture = ₹85.8 per kg

Desired profit = 30%

Concept Used:

The cost price of the mixture will be the weighted average of the costs of the two types of sugar, and the selling price includes the profit.

Formula Used:

Selling price = $$\text{Cost price} \times \left(1 + \frac {\text{Profit}}{ 100}\right)$$​​

Solution:

Let the quantity of sugar costing ₹74 per kg be x kg, and the quantity of sugar costing ₹41 per kg be y kg.

Selling price is ₹85.8, and the profit is 30%, so:

85.8 = Cost price $$\times (1 + 0.30)$$​​

Cost price =$$\frac{85.8}{1.30}$$​ = 66

So, the cost price of the mixture must be ₹66 per kg.

Now, 

​$$\frac{74x + 41y}{x + y} = 66$$​​

74x + 41y = 66(x + y)

74x + 41y = 66x + 66y

74x - 66x = 66y - 41y

8x = 25y

​$$\frac{x}{y} = \frac{25}{8}$$ 

Alternate Solution: 

​Selling price is ₹85.8 and profit 30%

Cost price =$$\frac{85.8}{1.30}$$​ = 66

Ratio = 25 : 8