A dishonest grocer professes to sell pure butter at cpst price, but he

Rephrasing;
The grocer is selling 100g of mixture(butter+fat) for $100. This $100 includes a 25% profit because he would have only spent $80 for 80g of butter and 0$ for 20g fat.
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Actually a better example would be;

Think that the grocer spent $100 for buying 100g pure butter. Now; in order to gain a profit of 25%, he will have to sell the same butter for $125.

How he would do that?

He would add 25g of fat(worth $0) to 100g of pure butter(worth $100) and sell 125g of mixture(butter+fat), saying that it is pure butter, for $125

Now you see;
125g of mixture is sold for $125 for which he had spent only $100. He made a profit of 25%.

125g of mixture contains 25g of fat; which is 25/125*100=20%

I got 20% as well.

Say 100g pure butter costs $100

But; $100 is his 25% profit because he just used 80gram pure butter.

80g would have costed him $80 and he sold it for $100 by adding 20g of freely available fat. $100 is 1.25(80)

so;
total weight=100g
fat=20g

20%

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%.

I am not too good with alligation;

But, you put the mean price of the mixture = 25%, which is not correct.
It should be 4/5

So the diagram should look like;

0 100
\ /
80
/ \
20 80

Top Right = C.P. of 100 units of pure butter; say $100
Top Left = C.P. of 100 units of freely available fat; $0

So; S.P. for 100 units of mixture(butter+adulterated fat)=$100

Mean price = C.P. of 100 units of mixture = (100/(100+Gain%))*S.P. = (100/(100+25))*100 = $80

Bottom Right = Units of butter in 100 units of mixture = (80-0)=80;
Bottom Left = Units of of freely available fat in 100 units of mixture = (100-80)=20

\(\therefore\) Ratio of "free fat:butter"= 20:80 = 1/4

% of free fat in the mixture = (1/(1+4))*100=20%

Ans: "A"

[quote="sonuindia88"]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?

A. 20%
B. 25%
C. 33.33%
D. 40%
E. 35%

hi

say, cost of producing pure butter is $100, and this dishonest grocer intends to sell the butter at $100, making a profit of 25%. It is possible as we know he will adulterate the butter by mixing some fat found free of cost
so far so good

now, if he gains a profit of 25%, selling the butter at $100, it is very natural to assume that

125% corresponds to 100, and
100% = 80

thus, actually he will sell $80 worth of pure butter rather than $100, and the remaining 20% will constitute artificial fat

so the answer is 20%

thanks
cheers through the kudos button if this helps

here is what i did
a is the butter and b is the fat
a / (a+b)=100%/125
125a=100 a +100b so 25 a=100b or a=4b
b/(a+4b)=b/5b=1/5
or 20%?

Actually can you tell me where I am doing wrong by using gain% in my method?

Hi

I was looking for a mistake in my approach...Somebody please help...In the method whr is the flaw?I am not able to figuare out

What does this mean :

But; $100 is his 25% profit because he just used 80gram pure butter.
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100 * (b + f) - 100 * b = (25/100) * 100 * b
b = 4 * f
Percentage of f = (f / (b + f)) * 100 = (f/5f) * 100 = 20%

Ans B - 25%

I did this with fairly little calculation.

Presume:
1. Cost of pure butter is $100/100 gms

We are told that the grocer mixed it with fat and thus gained 25% profit on the mixture.

Therefore, 25% profit must be coming from using fat instead of butter (fat is free of cost for him, as mentioned).

Thus, the mixture comprises of 75 gms pure butter and 25 gms fat!

let 100 be the selling cost
x(25/100+1)=100
5x/4=100
x=80
that means extra was 20 (A)

This is similar to how much up in percentage the seller should mark its item for 25% profit.
Sell price =1.25*Cost Price
Cost = 1/5/4*sell
cost=4/5*Sell
cost = 4/5sell
mark up = 1-4/5 = 1/5
=1/5*100 = 20 percent

The cost of the adulterated fat is 0.
The average cost of mixture to get 25% profit by selling at Cost Price.
Let the cost of the pure butter is 100.
Cost price of butter after mixed adulterated fat
= 100 x 100/125 = Rs. 80
Therefore, the ratio of the adulterated fat in pure butter is: (100-80)/(80-0)=1:4
= 1:4
The percentage of adulterated fat is 1/(1+4) *(100)=20%