# Q.7 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 3/2. Find the rational number.

Let the numerator of the rational number be x.

Then denominator will be x + 8.

Further, according to question,

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

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

Cross-multiplication gives:

2(x + 17)  =  3(x + 7)

or                   2x + 34  =  3x + 21

or                        x  = 13

Hence the rational number is   $\frac{13}{21}$.

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