Question

Two numbers are in ratio $5:3$ . If they differ by $18$ . What are the numbers?

Answer 1

Hint: If a ratio of two numbers is given as $x:y$ then it can also be written in terms of fraction as ${\displaystyle \frac{x}{y}}$ . We can write the numbers as $xk$ and $yk$ , where $k$ is constant which is common to both numbers when the ratio $x:y$ is given.

Complete step-by-step answer:
The given ratio of two numbers is $5:3$ and difference between these two numbers is $18$
Let us consider two numbers are $x\mathrm{\&}y$
The ratio of these number can be written as,
 ${\displaystyle \frac{x}{y}}={\displaystyle \frac{5}{3}}$
Then it can further simplified as,
 $x={\displaystyle \frac{5}{3}}y$ ….. (1)
The difference between these two numbers is given,
 $x-y=18$ ….. (2)
Put the value of $x$ from the equation $$\left(1\right)$$ in equation $$\left(2\right)$$ we have
 $x-y=18$
 ${\displaystyle \frac{5}{3}}y-y=18$
Further it can be simplified then we have,
 ${\displaystyle \frac{2}{3}}y=18\Rightarrow y=27$
Substituting the value of $y$ in equation $$\left(2\right)$$we have
 $$\begin{gathered} x-y=18 \\ x-27=18\Rightarrow x=45 \end{gathered}$$
Note: We can do this problem in an indifferent way which by considering numbers as $xk$ & $yk$ and putting these values in another equation and finding the value of $k$ then we can find numbers. Avoid any type of calculation mistake.