Question

A fraction becomes 9 by 11 when 2 in added to both newmarator and denominator and it becomes 5 by 6 when 3 is added to newmarator and denominator than find the fraction

Answer 1

◆AnSwEr-

Let the numerator= x

Let the denominator= y

Therefore, the fraction becomes $\frac{x}{y}$

Now,

According to the question,

$\frac{x+2}{y+2}=9\\=>\ x+2=9y+18\\=>\ 9y+16=x....................(1)$

And,

$\frac{x+3}{y+3}=\frac{5}{6}\\=>\ 6x+18=5y+15\\=>\ 5y-3=6x...................(2)$

Now, solving (1) and (2), we get-

$x=\frac{-107}{4}$

and,

$y=\frac{-19}{4}$

Therefore, the fraction is,

$\frac{x}{y}=\frac{\frac{-107}{4}}{\frac{-19}{4}}$

Therefore, the fraction is,

$\frac{107}{19}$

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