Question

A dishonest milkman prefers to sell his milk at cost price but he mixes it with water and thereby gains 25%. The percentage of water in the mixture is,
a. 4%
b. \[6\dfrac{1}{4}\]%
c. 20%
d. 25%

Answer 1

Hint: Take a total of 100L of milk. Assume ‘x’ as the milk added. Find the percentage of water which is mixed with the milk. Consider 25% gain as he added 25 liters of water. Find the % of water added in the mixture.

Complete step by step answer:

Let us assume that the milkman has 100 liters of milk. It is said that he mixes water with his milk.
Let us assume that the milkman adds ‘x’ liters of water into the milk. The percentage of water in the milk can be given as
(Amount of water added / Total amount of milk) \[\times \] 100.
\[\therefore \] Percentage of water in the milk \[=\dfrac{x}{100+x}\times 100\].
It is said that the milkman gains 25%. Let us assume that the milkman added 25 liter of water into the 100 liter of milk.
Then the percentage of water in milk \[=\left( \dfrac{25}{100+25} \right)\times 100\]

$ =\dfrac{25}{125}\times 100$
$ =20% $
Thus we got the percentage of water in the mix as 20%. Therefore, the percentage of milk in the mix = (100 - 20) % = 80%.
Thus in the new mixture, if the milk is 80%, then 80% of the total mixture should be 100 liters.
We know the total mixture = 100 + x.
\[\therefore \left( 100+x \right)80%=100\]
\[\Rightarrow \left( 100+x \right)\times \dfrac{80}{100}=100\] (Cross multiply and simplify it)
\[\begin{align}
  & \left( 100+x \right)80=100\times 100 \\
 & 100+x=\dfrac{100\times 100}{80} \\
 & 100+x=125 \\
 & \therefore x=125-100=25 \\
\end{align}\]
Thus we can find the percentage of water in the mixture = \[\dfrac{25}{\left( 100+25 \right)}\times 100=20%\].
Thus we got the percentage of water in the mixture as 20%.
\[\therefore \] Option (c) is the correct answer.

Note: We can solve using another method.
Let the cost price of milk be Rs.1.
\[\therefore \] Selling price of 1 liter of mixture = Rs.1
\[\therefore \] Gain = 25%.
CP of 1 liter mixture = Rs. \[\left( \dfrac{100}{100+25}\times 1 \right)=\dfrac{4}{5}\].
\[\therefore \] Ratio of milk to water \[=\dfrac{4}{5}:\dfrac{1}{5}=4:1\]
 \[\therefore \] Percentage of water in mixture \[=\left( \dfrac{1}{5}\times 100 \right)%=20%\].