In what ratio should sugar costing ₹10 per kg be mixed with sugar costing ₹86 per kg so that by selling the mixture at ₹83.2 per kg, there is a profit of 30%?

Correct option is B

Given:

Cost of the first type of sugar = ₹10 per kg

Cost of the second type of sugar = ₹86 per kg

Selling price of the mixture = ₹83.2 per kg

Profit = 30%

Solution:

Let the ratio of the first sugar to the second sugar be x : y.

Cost price of the mixture =$$\frac{10x + 86y}{x + y}$$​​

Since the selling price gives a profit of 30%, we can calculate the cost price using:

Cost price of the mixture $$= \frac{83.2}{1 + \frac{30}{100}} = \frac{83.2}{1.3} = 64$$​

Now, we have the equation for the cost price of the mixture:

​$$\frac{10x + 86y}{x + y} = 64$$​

10x + 86y = 64(x + y)

10x + 86y = 64x + 64y

-54x + 22y = 0

​$$\frac{x}{y} = \frac{22}{54}$$​

Therefore, the ratio of the first type of sugar to the second type of sugar is 22 : 54.