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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

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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.

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  • $\begingroup$ Yes, this is the answer, Thanks :) $\endgroup$ – Sanjay Verma Sep 8 '20 at 7:45

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