Question

To make a cup of tea, the ratio of water to milk is 3 : 1. So, to make 4 cups of tea, the ratio of water to milk is :
A. 4 : 3 : 1
B. 12 : 1
C. 12 : 4
D. 4 : 12

Answer 1

Hint: Use the given information and assume the volume of water in the tea as $3x$ and volume of milk in the tea as $x$. Using the unitary method, find the volume of water and milk in 4 cups of tea by multiplying 4 with the volume of water and milk in 1 cup of tea. Take the ratio and cancel $x$ from both the volumes and get the answer.

Complete step by step answer:
Here, we have been given that the ratio of volume of water to milk in one cup of tea is 3 : 1 and we have to determine the ratio of their volumes in 4 cups of tea. Now since, the volume ratio of water to milk in a cup of tea is 3 : 1, therefore the volume of water can be assumed as $3x$ and volume of milk as $x$. Therefore,
For 1 cup of tea, we have,
Volume of water = $3x$
Volume of milk = $x$
So, for 4 cups of tea, using unitary method, we have,
Volume of water = $4\times 3x=12x$
Volume of milk = $4\times x=4x$
Therefore, considering the ratio of volume of water to milk for 4 cups of tea, we get,
$\dfrac{\text{Volume of water}}{\text{Volume of milk}}=\dfrac{12x}{4x}$
Cancelling factor $x$ from both the numerator and the denominator, we get,
$\begin{align}
  & \dfrac{\text{Volume of water}}{\text{Volume of milk}}=\dfrac{12}{4} \\
 & \therefore \text{Ratio}=12:4 \\
\end{align}$
Hence, option C is the correct answer.

Note:
One may note that the simplified form of 12 : 4 will be 3 : 1. This is because whatever number of cups of tea will be, the ratio will always be 3 : 1 in simplified form. If there would have been $n$ cups of tea, then the ratio would have been $3n:n$. Also, note that here, we do not have to worry about the unit of volume because the ratios are taken, so whatever may be the volume unit, it will get cancelled.