In what ratio should sugar costing ₹10 per kg be mixed with sugar costing ₹61 per kg sothat by selling the mixture at ₹31.5 per kg, there is a profit of 26%?

Correct option is B

Given:

Cost of sugar 1: ₹10 per kg

Cost of sugar 2: ₹61 per kg

Selling price of the mixture: ₹31.5 per kg

Profit: 26%

Formula Used:

Allegation formula:

​$$\frac{(C_2 - C_m)}{(C_m - C_1)}$$​​

Where:

$$C_1$$​ = Cost of first sugar,

$$C_2$$​ = Cost of second sugar,

$$C_m$$​ = Cost of mixture

Cost price = $$\frac{\text{Selling Price}}{1 +\text{ Profit Percentage}}$$​​

Solution:

Cost price = $$\frac{31.5}{1 + 0.26} = \frac{31.5}{1.26} = 25$$​​

Cost price = ₹25 per kg

Now, apply the allegation method:

​$$\frac{(61 - 25)}{(25 - 10)} = \frac{36}{15} = 12:5$$​​

Thus, the two types of sugar should be mixed in the ratio of 12 : 5

Alternate Solution: ​

Cost Price of mixture = ₹25 

By allegation --