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The sum of two numbers is 2490 . If $6.5 \%$ of one number be equal to $8.5 \%$ of the other, then find the numbers.

Solution

Let the numbers are $x$ and $y$. By the question

$x+y=2490$

Again,

$6.5 \%$ of $x=8.5 \%$ of $y$ $\Rightarrow \quad \frac{6.5 x}{100}=\frac{8.5 y}{100}$ $\Rightarrow \quad 65 x=85 y$ $\Rightarrow \quad 13 x=17 y$

$\therefore \quad x=\frac{17}{13} y$

$\therefore$ By the question,

$$\begin{array}{l} x+y=2490\\6.5 \% \text { of } x=8.5 \% \text { of } y \end{array}$$
Putting the value of $x$ in eqn. (1),
\begin{aligned} & \frac{17}{13} y+y=2490 \\ \Rightarrow & 30 y=2490 \times 13 \\ \therefore \quad & y=\frac{2490 \times 13}{30} \\ &=83 \times 13=1079 \end{aligned}
Putting the value of $y$ in eqn. (2).
$$x=\frac{17}{13} \times 1079=17 \times 83=1411$$
$\left.\therefore \begin{array}{l}\text { Ist no. }=1411 \\ 2 \text { nd no. }=1079\end{array}\right\}$;Ans.

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