Question

The Sum of two numbers is 2490. If 6.5% of one number is equal to 8.5% of the other, Find the Numbers.​

Answer 1

Answer:

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Answer 2

$\large\underline{ \underline{ \sf \maltese{ \: Question:- }}}$

• The Sum of two numbers is 2490. If 6.5% of one number is equal to 8.5% of the other, Find the Numbers.

$\large\underline{ \underline{ \sf \maltese{ \: Assume:- }}}$

• Let the First Number be x
• Second Number = 2490 - x

$\large\underline{ \underline{ \sf \maltese{ \: Given:- }}}$

• Sum of Two Numbers = 2490

• 6.5% of the First Number $\bf \: \frac{6.5}{100} \times \: x \: = \: \boxed{ \frac{65x}{1000} }$
• 8.5% of the Second Number $\bf \: \frac{8.5}{100} \times \: (2490 - x)\: = \: \boxed{ \frac{85}{1000}(2490 - x) }$

It is given that 6.5% of the First Number is equal to 8.5 of the other

$\large\underline{ \underline{ \sf \maltese{ \: Solution :- }}}$

$\begin{gathered} \begin{gathered}\underline {\boldsymbol{ ☯ \: According\: to \:the\: Question \: ☯}} \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\begin{gathered}: \implies \underline\blue{ \boxed{\displaystyle \sf \bold\orange{\: \frac{65x}{1000} \: = \: \frac{85}{1000} (2490 - x) }} }\\ \\\end{gathered}\end{gathered}\end{gathered}$

Multiplying both Sides by 1000

$\qquad \quad {:} \longrightarrow \sf{\sf{65x \: = \: 85(2490 - x) }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{65x \: = \: 2490 \: \times \: 85 \: - \: 85x}}$

$\qquad \quad {:} \longrightarrow \sf{\sf{65x \: + \: 85x \: = \: 2490 \: \times \: 85 \: }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{150x \: = \: 2490 \: \times \: 85 \: }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{x \: = \: \frac{2490 \: \times \: 85}{150} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{x \: = \: 1411 }}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{x \: = \: 1411 }}}$

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• First Number = x = 1411
• Second Number = 2490 - 1411 = 1079

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$\large\underline{ \underline{ \sf \maltese</strong><strong>\</strong><strong>g</strong><strong>r</strong><strong>e</strong><strong>e</strong><strong>n</strong><strong>{ \: </strong><strong>Verfication\</strong><strong>:</strong><strong> </strong><strong>1</strong><strong>\</strong><strong>:</strong><strong> </strong><strong> :- }}}$

$\underbrace\red{\boxed{ \sf \purple{ 6.5 \% \: of \: first \: number}}}$

$\qquad \quad {:} \longrightarrow \bf{\bf{6.5\% \: of \: first \: number \: = \: \frac{6.5}{100} \times 1411 }}$

$\qquad \quad {:} \longrightarrow \bf{\bf{6.5\% \: of \: first \: number \: = \: \frac{65 \: \times \: 1411}{1000} }}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{ 6.5\% \: of \: first \: number \: = \: \frac{91715}{1000} }}}$

$\underbrace\red{\boxed{ \sf \purple{ 8.5 \% \: of \: first \: number}}}$

$\qquad \quad {:} \longrightarrow \bf{\bf{8.5\% \: of \: first \: number \: = \: \frac{8.5}{100} \times 1079 }}$

$\qquad \quad {:} \longrightarrow \bf{\bf{8.5\% \: of \: first \: number \: = \: \frac{85 \: \times \: 1079}{1000} }}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{ 8.5\% \: of \: first \: number \: = \: \frac{91715}{1000} }}}$

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Clearly , 6.5% of the First Number is equal to 8.5 of the Second Number , which is the same as given in the Problem

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$\large\underline{ \underline{ \sf \maltese\green{ \: Verfication\: 2\: :- }}}$

$\quad {:} \longrightarrow \bf{\bf{Sum \: of \: First \: and \: Second \: Numbers \: = \: 2490 }}$

$\quad {:} \longrightarrow \bf{\bf{1411\: + \: 1079 \: = \: 2490 }}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{ 2490 \: = \: 2490 }}}$

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$\begin{gathered}\begin{gathered}\qquad \therefore\: \sf{ First \: Number \: = \underline {\underline{ 1411}}}\\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\qquad \therefore\: \sf{ Second \: Number \: = \underline {\underline{ 1079}}}\\\end{gathered}\end{gathered}$

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