The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is 121. Find the number.
Given:
The denominator of a rational number is greater than its numerator by 8.
The numerator is increased by 17 and the denominator is decreased by 1, the number obtained is 121.
To do:
We have to find the original fraction.
Solution:
Let the numerator of the original fraction be $x$.
This implies,
The denominator of the original fraction$=x+8$
The original fraction$=\frac{x}{x+8}$.
The numerator is increased by 17 and the denominator is decreased by 1.
This implies,
New fraction$=\frac{x+17}{x+8-1}=\frac{x+17}{x+7}$
According to the question,
The number obtained is 121.
$\Rightarrow \frac{x+17}{x+7}=121$
$x+17=121(x)+121(7)$
$121x-x=17-847$
$120x=-830$
$x=\frac{-830}{120}$
$x=\frac{-83}{12}$.
Therefore, the original fraction is $\frac{-83}{12}$.
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