Question

The denominator of a fraction exceeds its numerator by 8 if the two numerator is increased by 17 and the denominator is decreased by 1 we get 3 by 2 find the original fraction

Answer 1

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Answer 2

Solution :

Let the numerator of Original Fraction = x

According to question , denominator = x + 8

Therefore , the original fraction = $\italic{\bf{\frac{x }{x + 8}}}$

Now increased 17 to numerator and decreased 1 from denominator

$\implies \bold{\frac{x + 17}{x + 8 - 1} } = \bold{\frac{3}{2} }$

$\implies \bold{\frac{x + 17}{x + 7 } = \bold{\frac{3}{2}}}$

$\implies \bold{2(x + 17) = \bold{3(x + 7) }}$

$\implies \bold{2x + 34 = \bold{3x + 21 }}$

$\implies \bold{3x - 2x = 34 - 21}$

$\implies \bold{ x = 13 }$

Therefore , Numerator = 13 and denominator = 13 + 8 = 21

So Original Fraction = $\bold{\frac{13}{21} }$   Answer