Question

A mixture of 40 liters of milk and water contains 10% water. How much water is to be added to the mixture so that the water may be 20% of the new mixture.
(a)5 liters
(b)4 liters
(c)6.5 liters
(d)7.5 liters

Answer 1

Hint: We will solve this question by calculating the amount of water in liters in the mixture at the present and then applying the given 20% of water

Complete step by step answer:
We are given that the mixture has 40 liters of milk and water.
Given that in this mixture of 40 liters, the water content is 10%.
We will calculate this 10% of water in terms of liters, basically we need to determine the present amount of water in a given 40 liters mixture.
Given that 40 liters of mixture contains 10% of water implies in liters the quantity of water will be,
\[\left( 10\% \right)40\]
Gives the amount of water is = \[\left( \dfrac{10}{100} \right)40\]
Gives the amount of water is = \[\dfrac{400}{100}\]
[\Rightarrow\] The amount of water is 4 liters.
 So, the content of water at present is 4 liters.
Let us suppose we add x liters of water to make the percentage of water in the mixture increase to 20%, then after adding x liters the new water content will be,
$4+x = (4+x)$ liters.
Adding this $x $ amount of water to the mixture the total content of the mixture will increase and will become,
$40+x = (40+x)$ liters.
Now we equate the percentage of water in the new mixture which is given by
\[\left( \dfrac{4+x}{40+x} \right)100\]
 to 20 because we needed 20% of water and we are already converting the term
\[\left( \dfrac{4+x}{40+x} \right)100\]
 into percent so we don’t need to add “%” with 20 on the right hand side.
Equating both we get,
\[\left( \dfrac{4+x}{40+x} \right)100=20\]
We will now solve for the variable x,
\[\begin{align}
  & \left( \dfrac{4+x}{40+x} \right)100=20 \\
 & \Rightarrow \left( \dfrac{4+x}{40+x} \right)5=1 \\
 & \Rightarrow \dfrac{4+x}{40+x}=\dfrac{1}{5} \\
 & \Rightarrow 20+5x=40+x \\
 & \Rightarrow 4x=20 \\
 & \Rightarrow x=\dfrac{20}{4} \\
\end{align}\]
Gives the value of x = 5 liters.

Therefore, the new amount of water to be added in the mixture to make the water content 20% in the mixture is 5 liters i.e. option (a).

Note:
The possibility of error in the question is that while calculating the value of x by equating the two values
\[\left( \dfrac{4+x}{40+x} \right)100\]
 and 20 you can go for dividing the right hand side of the equation, that is, 20 by 100, which is wrong because we already have multiplied
\[\left( \dfrac{4+x}{40+x} \right)\]
 by 100 converting it into percentage, so any other addition on the right hand side will lead to an incorrect solution.