Question

Two numbers are in the ratio 3:5. if 9 be subtracted from each ,them they are in the ratio 12:23 find the second number​

Answer 1

Given: Two numbers are in the ratio 3:5.

Need To find: The second number.

❒ Let the two numbers be 3x and 5x respectively.

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$\underline{\boldsymbol{\bigstar{\;\: According\: to \:the\: Question :}}}$

• If 9 be subtracted from each of them they are in the ratio 12:23.

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Therefore,

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$:\implies\sf \dfrac{3x - 9}{5x - 9} = \dfrac{12}{23} \\\\\\:\implies\sf 23(3x - 9) = 12(5x - 9) \\\\\\:\implies\sf 69x - 60x = 207 - 108\\\\\\:\implies\sf 9x = 99\\\\\\:\implies\sf x = \cancel\dfrac{99}{9}\\\\\\:\implies{\underline{\boxed{\frak{\pink{x = 11}}}}}\;\bigstar$

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$\underline{\bf{\dag} \:\mathfrak{Finding \: both \; numbers\: :}}$⠀⠀⠀⠀

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• First number, 3x = 3(11) = 33

• Second number, 5x = 5(11) = 55

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$\therefore{\underline{\sf{Hence,\; the \; required\: second \; number \; is \; \bf{55 }.}}}$

Answer 2

Answer:

Given :-

• Two number are in ratio 3:5
• When 9 subtracted from both then ratio become 12:23

To Find :-

Second Number

Solution :-

Let the number be 3a and 5a

$\sf \: \dfrac{3a - 9}{5a - 9} = \dfrac{12}{23}$

By Cross Multiplication

$\sf \: 23(3a - 9) = 12(5a - 9)$

$\sf \: 69a - 207 = 60a - 108$

$\sf \: 69a - 60a = 207 - 108$

$\sf \: 9a = 99$

$\sf \: a \: = \dfrac{99}{9}$

$\sf \: a \: = 9$

${ \textsf{ \textbf{ \underline{Second \: Number = 5(9) = 45}}}}$