### Theory:

As one amount increases, another amount increases at the same rate or as one amount decreases, and another amount decreases at the same rate, which is known as direct proportional.
Two quantities, $$x$$ and $$y$$, are directly proportional if $$x \propto y$$ $$\Rightarrow \frac{x}{y}=k$$ where $$k$$ is positive. We can also write it as $$\frac{x_1}{y_1} = \frac{x_2}{y_2}$$ where $$x_1, x_2$$ are values of $$x$$ corresponding to $$y_1,y_2$$ are values of $$y$$.
Example:
You are paid $$₹50$$ per hour. How many hours would you have worked to reach the amount of $$₹300$$?

Solution:

Let the number of hours worked be $$x$$.

Logically, if $$1$$ hour $$= ₹50$$, then to reach the amount of $$₹300$$, you need to work more hours.

Thus, an increase in one quantity causes an increase in other quantity also. This is a direct proportion.

Let us use the formula $$\frac{x_1}{y_1} = \frac{x_2}{y_2}$$.

Here, $$x_1$$, $$x_2$$ denotes the hours and $$y_1$$, $$y_2$$ denotes the amount.

Substituting the known values, we have:

$$\frac{1}{50} = \frac{x}{300}$$

$$x = \frac{300}{50}$$

$$x = 6$$

Therefore, you must work $$6$$ hours to reach the amount of $$₹300$$.