In what ratio must Suhail, a wholesaler, mix wheat worth ₹45 per kg with wheat worth ₹75 per kg, so that by selling the mixture at ₹80 per kg, he may gain 25%?

Correct option is A

Given:
Price of wheat 1 = ₹45/kg
Price of wheat 2 = ₹75/kg
Selling price of mixture = ₹80/kg
Profit percentage = 25%

Formula Used:

SP= $$\text{CP} \times \left( 1 + \frac{\text{Profit\%}}{100} \right)$$​​

Solution:

Since the selling price of the mixture gives a 25% profit, we can find the cost price (CP) of the mixture using:
SP =$$\text{CP} \times \left( 1 + \frac{\text{Profit\%}}{100} \right)$$​​
80 = CP $$\times$$​ $$\left( 1 + \frac{\text{25}}{100} \right)$$​​
80 = CP$$\times$$1.25​
CP = $$\frac{80 }{ 1.25 }$$​= ₹64/kg
Apply the alligation method:

The ratio of the quantities of wheat 1 and wheat 2 is given by the differences calculated above:
Ratio = 11 : 19
Therefore, Suhail must mix the two types of wheat in the ratio 11 : 19.

Option (A) is right.