# Pinku a dishonest grocer professes to sell pure butter

Pinku a dishonest grocer professes to sell pure butter at cost price, but he mixes it with adulterated fat and thereby gains 25%. Find the percentage of adulterated fat in the mixture assuming that adulterated fat is freely available.

TBH I don't understand how to solve this but I've tried something please advice:

let the cost price of the end product(fat + butter) be $$x$$.

$$\therefore$$ selling price will be $$1.25x$$ and ratio of butter mixed with fat will be $$(m_1*y+m_2*0)/m_1+m_2 =x$$

where $$m_1$$ is quantity of butter and $$m_2$$ is quantity of fat and $$y$$ is original cost price of butter.

I don't understand how to proceed further because information given in questions is very less. please help

It's not very clear what the question means. I assume that he makes a $$25\%$$ profit when selling one pound of "butter". Since he pays for however much butter he uses, but adulterated fat is free, his cost is $$xp$$, where $$x$$ is the proportion of butter he uses and $$p$$ is the price per pound of pure butter, and he receives $$p$$ for it. So we need $$p=1.25xp$$, or $$x=1/1.25=0.8$$.
Therefore his product is $$80\%$$ butter and $$20\%$$ adulterated fat.