Question

Two numbers are in the ratio 5 : 9. on subtracting 3 form each, the ratio becomes 1 : 2. Find the numbers​

Answer 1

Given :-

• Ratio of two numbers is 5:9
• on subtracting 3 from each number then, their ratio becomes 1:2

To Find :-

• find the numbers ?

Solution :-

let the two numbers are 5x and 9x

on substracting 3 from each number, then numbers are

• 5x - 3
• 9x - 3

and according to the question (on substracting 3 from each number then their ratio becomes 1:2)

$\bold{: \implies \frac{5x - 3}{9x - 3} = \frac{1}{2} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies 2(5x - 3) = 1(9x - 3) } \\ \\ \bold{: \implies 10x - 6 = 9x - 3} \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies 10x - 9x = - 3 + 6 } \: \: \: \: \: \: \\\ \\ \bold{: \implies x = 3} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

then, number are

• 5 × 3 = 15
• 9 × 3 = 27

hence, the two numbers are 15 and 27

Answer 2

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

• Two numbers are in the ratio 5 : 9. on subtracting 3 from each, the ratio becomes 1 : 2. Find the numbers

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

• Ratio of 2 Number = 5 : 9 and 3 is Substracted from from both the ratio. The new number formed is in the ratio 1 : 2.

$\large\underline{ \underline{ \sf \maltese{ \: To \: Find :- }}}$

• Find the Numbers .

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

• Let the First Number be 5x
• Let the Second Number be 9x

Now, subtracting 3 from each number

• First New = 5x - 3
• Second Number = 9x - 3

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

$\qquad \quad {:} \implies { \boxed{ \sf{\bf{ \frac{5x - 3}{9x - 3} \: = \: \frac{1}{2} }}} }$

Now, doing Cross Multiplaction :-

$\qquad \quad {:} \longrightarrow \sf{\sf{ 2(5x-3)\: =\: 1(9x-3) }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ 10x \: - \: 6 \: = \: 9x \: - \: 3 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ 10x \: - \: 9x\: = \: 6 \: - \: 3 }}$

$\qquad \quad {:} \longrightarrow \sf{ \boxed{\sf{ x\: = \: 3 }}}$

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Therefore :-

$\longmapsto\tt{First\:Number=5\: \green\times \: x}$

$\qquad \quad {:} \longrightarrow \sf{\sf{5\: \times \: 3}}$

$\qquad \quad {:} \longrightarrow \sf{ \boxed{\bf{First \: number \: = \: 15}}}$

$\longmapsto\tt{Second\:Number=9\: \green\times \: x}$

$\qquad \quad {:} \longrightarrow \sf{\sf{9\: \times \: 3}}$

$\qquad \quad {:} \longrightarrow \sf{ \boxed{\bf{Second\: number \: = \: 27}}}$

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So, The 2 Number are 15 and 27.

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