A dishonest grocer professes to sell pure butter at cpst 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?
I am doing this by alligation using gain%
On selling at CP gain %=0
On selling adulterated fat gain%=100
Required gain =25
Hence using graphical approach
hence ratio of pure butter and adulterated fat x:y=75:25
% of adulterated fat in mixture 1/4*100=25%
Please tell me where I am doing wrong?
Alligation is used to find the average value given two values and the ratio of their weights. First of all, if average profit is 25%, what is the profit on the two individual items?
Profit on pure butter sold at cost price = 0%
What about profit on adulterated fat which is available free of cost? How is it 100%? Since its cost price is 0 and profit % = profit/CP * 100, profit% is actually infinite.
Secondly, the ratio that you get when you use alligation will be the ratio of their cost price, not the amount in which they are added. You need to be very careful about the weights you use.
When you are averaging Profit%, the weight will be Cost price because Profit% = Profit/Cost Price. Since denominator has total weight, weights will be cost price. Hence, do not use alligation in this question.
It can be very easily done using the method suggested above. Since profit is 25%, $4 of cost price gives $1 of profit. If cost of pure butter is $1 per gm, he used only 4 gm butter but sold 5 gm mixture. So 1 out of every 5 was adulterated fat i.e. 20%.
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