Question

A milk vendor mixes water with pure milk in the ratio of $1:3$ while processing it. The vendor dispatches $50\text{L}$ of the mixed milk each day. Determine the total quantity of mixed milk in terms of quantity of pure milk used. Is this a function?

• A. Yes, this is a non-linear function.
• B. This is not a linear function as three variables are involved.
• C. Total quantity of mixed milk is four-third of the quantity of pure milk.
• D. Total quantity of mixed milk is two-third of the quantity of pure milk.

Answer 1

The correct option is C Total quantity of mixed milk is four-third of the quantity of pure milk.

Let the quantity of pure milk is represented by $x\text{L},$ and the quantity of water by $w\text{L}.$

It is given that $\text{Quantity of water}:\text{Quantity of pure milk}=1:3$
$\Rightarrow w:x=1:3$
$\Rightarrow \frac{w}{x}=\frac{1}{3}$
(by cross-multiplying)
$\Rightarrow w=\frac{x}{3}$

Let, the total quantity of mixed milk is represented by $y\text{L}.$
Now, $\text{Total quantity of mixed milk}=\text{Quantity of water}+\text{Quantity of pure milk}$
$\Rightarrow y=w+x$
$\Rightarrow y=\frac{x}{3}+x$
$\Rightarrow y=x(\frac{1}{3}+1)$
$\Rightarrow y=\frac{4}{3}x$
This is the required relationship between the total quantity of mixed milk and the quantity of pure milk.

This is a linear function as $y$ has a single value for a particular $x.$