### Theory:

In direct proportion, two quantities $$x$$ and $$y$$ are said to increase (or decrease) together in such way that the ratio of their respective values is constant.

That is to suggest, if $$\frac{x}{y} =$$ $$k$$ is positive, then $$x$$ and $$y$$ will differ directly. That is, $$x$$ and $$y$$ are in direct proportion.
When the quantities $$x$$ and $$y$$ are in direct proportion, we can write $\frac{{x}_{1}}{{x}_{2}}$ $$=$$ $\frac{{y}_{1}}{{y}_{2}}$. Where ${y}_{1}$, ${y}_{2}$ are values of $$y$$ corresponding to the values ${x}_{1}$, ${x}_{2}$ of $$x$$.
Example:
If $$1$$ part of a sugar requires $$75 mL$$ of water, how much part of sugar should we mix with $$1800 mL$$ of water?

Let the parts of sugar mix with $$1800 mL$$ water be $$x$$.

Practically, if $$1$$ part of a sugar requires $$75 mL$$, of water, then $$1800 mL$$ of water requires more sugar.

Increase in quantity of water increases the quantity of sugar. So it is in direct proportion.
When the quantities $$x$$ and $$y$$ are in direct proportion, we can write $\frac{{x}_{1}}{{x}_{2}}$ $$=$$ $\frac{{y}_{1}}{{y}_{2}}$. Where ${y}_{1}$, ${y}_{2}$ are values of $$y$$ corresponding to the values ${x}_{1}$, ${x}_{2}$ of $$x$$.
Substitute the known values in the formula.

$$\frac{1}{75}$$ $$=$$ $$\frac{x}{1800}$$

$$75$$ $×$ $$x$$ $$=$$ $$1$$ $×$ $$1800$$

$$x =$$ $$\frac{1800}{75}$$

$$x =$$ $$24$$

Hence, $$24$$ parts sugar should be mixed with the water of $$1800 mL$$.