Question

20 liter of a mixture contains milk and water in the ratio \[5:3\]. If \[4\] liters of this mixture is replaced by \[4\] liters of milk, the ratio of milk in the new mixture would be
A. \[2:1\]
B. \[7:3\]
C. \[8:3\]
D. \[4:3\]

Answer 1

Hint: From the given question we have been asked to find the ratio of milk in the new mixture where \[4\] liters of this mixture is replaced by \[4\] liters of milk. So, for solving these kinds of mixture problems we will use the given condition in the question, in this question we will use the condition milk and water in the ratio \[5:3\] and we will use the basic mathematical operations like addition and solve the questions.

Complete step by step solution:
We are given that the mixture contains milk and water in the ratio \[5:3\].
So, Let the amount of water and milk in the \[20\] liter of mixture is \[3x\] and \[5x\].
If four liter of mixture is replaced by four liter of milk then we get,
\[\Rightarrow milk=5x+4\]
\[\Rightarrow water=3x\]
Now we will equate this total amount of new milk and water to the total composition of mixture that is \[20\].
So, we get the equation as follows when we equate milk and water to total composition,
\[\Rightarrow 5x+4+3x=20\]
Now we will send the two to the other side of the equation and simplify the equation.
\[\Rightarrow 5x+3x=20-4\]
\[\Rightarrow 8x=16\]
\[\Rightarrow x=2\]
Now, the ratio of milk and water will be as follows.
\[\Rightarrow \dfrac{5x+4}{3x}\]
\[\Rightarrow \dfrac{5\times 2+4}{3\times 2}\]
\[\Rightarrow \dfrac{14}{6}\]
\[\Rightarrow \dfrac{7}{3}\,or\,7:3\]

So, the correct answer is “Option B”.

Note: Students should not make any mistake in calculations. Students should have good knowledge in mixture problems. We should not do mistakes like if we write the ratio of milk and water as \[ \dfrac{3x+4}{5x}\] instead of \[ \dfrac{5x+4}{3x}\] then our solution will be wrong.