Question

the dinominator of a fraction is 5 more than the numerater . if the numerator is increased by 18 and the denominator is increased by 4 the fraction becomes 25/8.find the fraction​

Answer 1

☯ Let the Numerator of fraction be x.

☯ Then, the denominator of fraction is = (x + 5).

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${\underline{\sf{\bigstar\; According\;to\; Question\;:}}}$

⠀⠀⠀⠀⠀☯ If the numerator is increased by 18 and the denominator is increased by 4 the fraction becomes 25/8.

$:\implies\sf \dfrac{x + 18}{(x + 5) - 4} = \dfrac{25}{8}$

$:\implies\sf \dfrac{x + 18}{x + 1} = \dfrac{25}{8}$

$:\implies\sf 8(x + 18) = 25(x + 1)$

$:\implies\sf 8x + 144 = 25x + 25$

$:\implies\sf 8x - 25x = 25 - 144$

$:\implies\sf - 17x = - 199$

$:\implies\sf x = \cancel{ \dfrac{- 199}{- 17}}$

$:\implies{\boxed{\frak{\pink{x = 7}}}}\;\bigstar$

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Therefore,

• Numerator of fraction, x = 7

• Denominator of fraction, (x + 5) = 7 + 5 = 12