Question

Two numbers are in the ratio $5:3$ if they differ by $18$ what are the numbers.

Answer 1

Calculating the two unknown numbers:

The given ratio is $5:3$.

Consider two numbers $5\mathrm{y}$ and $3\mathrm{y}$, such that $\mathrm{y}$ is a common multiple of two numbers.

The difference between the two numbers is given as $18.$

$$\begin{gathered} \Rightarrow 5\mathrm{y}-3\mathrm{y}=18 \\ \Rightarrow 2\mathrm{y}=18 \\ \Rightarrow \mathrm{y}=\frac{18}{2} \\ \Rightarrow \mathrm{y}=9 \end{gathered}$$

Substituting the value of $y$ in the two numbers $5y$ and $3y$:

$$\begin{gathered} 5\mathrm{y}=5\times 9 \\ \Rightarrow 5\mathrm{y}=45 \end{gathered}$$

$$\begin{gathered} 3\mathrm{y}=3\times 9 \\ \Rightarrow 3\mathrm{y}=27 \end{gathered}$$

Hence, the two numbers are $45$ and$27$.