Question

the denominator of a fraction exceeds its numerator by 5. if 2 is added to both numerator and the denominator, the fraction become4/5. find the fraction

Answer 1

Answer -

$\huge\frac{18}{23}$

Explaination :

→ Consider the numerator as x

Account to the question the first fraction =

$\large= > \frac{x}{x + 5}$

→ If 2 is added to them it is = 4/5

Equation :

$\large = > \frac{x + 2}{x + 5 + 2} = \frac{4}{5}$

$\large= > \frac{2 + x}{7 + x} = \frac{4}{5}$

$\large= > 5(2 + x) = 4(7 + x)$

$\large= > 10 + 5x = 28 + 4x$

$\large= > 5x - 4x = 28 - 10$

$\large{\green{\boxed{\green{\boxed{\red{\textsf{ x = 18 }}}}}}}$

So, the fraction =

$\large= > \frac{18}{23}$

→ Let's check if it meets the condition that the fraction is 4/5 after adding 2 to denominator and numerator.

$\large= > \frac{18 + 2}{23 + 2}$

$\large = > \frac{20}{25}$

Reduce them :

$\large= > \frac{4}{5}$

Therefore the fraction is :

$\huge = > \frac{18}{23}$

Answer 2

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