I am really confused about how this question has been solved. I've given the question, author's approach and then mine. Can you help me figure out why/ why not I have gone wrong?
Thanks in advance,
Suraj
Question
A milkman has 20 L of milk. He mixes 5 L of water in 20 L of pure milk. If the cost of pure milk is $18/L, then the profit of the milkman, when he sells the diluted milk at cost price is:
A) 20% B) 25% C) 33.33% D) 18%
The Author's approach
% Profit= 5/20=0.25=25%
My approach
The weighted percentage of milk in the new mixture=
{(1*20)+ (0*5)}/25
=0.8
=80% milk
% profit=
{(25)- (25*0.80)}/(25*0.80) where (25*0.80)= Actual price of diluted milk
=25%
You made an arithmetic error when you calculated $\frac{1\cdot 20+0\cdot 5}{25}=\frac{20+0}{25}=\frac{4}{5}=0.8\neq 0.83$
Indeed, making the correction, you should arrive at:
$\frac{25-25\cdot 0.8}{25\cdot 0.8} = \frac{25-20}{20}=\frac{5}{20}=0.25$ as expected.