Question

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

Answer 1

Given :  A dishonest grocer professes to sell pure butter at cost price, but he mixes it with adulterated fat and thereby gains 25%.  adulterated fat is freely available

To find : the percentage of adulterated fat in the mixture

Solution:

Let say cost price   = Rs C  per  kg

Selling Price = Rs C per kg

Butter  =   B  kg

Total Cost Price = BC  rs

Gain = 25 %  = (25/100)BC  

Total Sell Price = BC + (25/100)BC  =  125BC /100

Let say  X  % fat is mixed    

Then Mixture will be =    B   + (X/100)B   =  B (100 + X)/100  kg

SP =  Rs C per kg

Total Sell price = BC (100 + X)/100

125BC /100 = BC (100 + X)/100

=> 125 = 100 + X

=> X = 25

adulterated  FAT = 25 %  = (25/100)B  = 25B/100

Mixture  =   B (100 + X)/100  = B(125/100)

% of  adulterated fat in the mixture  = 100 *  ( 25B/100)/B(125/100)

= 20 %

20 % of adulterated fat is in the mixture

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