Question

Frame and solve the equations for the following statements:
Two numbers are in the ratio $5:3$. If they differ by $18$, what are the numbers?

Answer 1

Let the numbers be $x$ and $y$

Now, Difference is $18$

$\Rightarrow x-y=18$......................................(1)

and assuming that $x$ is the Larger number

and $\frac{5}{3}=\frac{x}{y}\to y=\frac{3x}{5}$

Putting $y=\frac{3x}{5}$ in eq(1) we get

$\Rightarrow x-\frac{3x}{5}=18\to \frac{2x}{5}=18\to x=45$

So, $45-y=18\to y=63$

Hence, the numbers are $45$ and $63$.