In what ratio should sugar costing Rs. 78 per kg be mixed with sugar costing Rs. 36 per kg so that by selling the mixture at Rs. 86.8 per kg, there is a profit of 24%?

Correct option is B

Given:

Cost price of first type of sugar = Rs. 78/kg

Cost price of second type of sugar = Rs. 36/kg

Selling price of the mixture = Rs. 86.8/kg

Profit = 24%

Formula Used:

Cost Price of Mixture = $$\frac{\text{Selling Price}}{1 + \frac{\text{Profit}}{100}}$$​​

Ratio = $$\frac{M - C_1}{C_2 - M}$$​​

where $$C_1$$​ = cost of cheaper sugar,

$$C_2$$​ = cost of dearer sugar,

M = mean price or cost price of mixture.

Solution:

Cost Price of Mixture = $$\frac{86.8}{1 + \frac{24}{100}}$$​​

​$$= \frac{86.8}{1.24} = 70$$​​

Now, apply the allegation rule:

Ratio = $$\frac{70 - 36}{78 - 70} = \frac{34}{8}$$​​

The sugar should be mixed in the ratio 34 : 8 

Alternate Solution: ​

Cost price of mixture = ₹70/kg 

Allegation rule;