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# 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 \frac { 3 }{ 2 }. Find the rational number.

Let the numerator be x.
and denominator be y

As given y= (x + 8)

Also as per the conditions given, we have

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

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

$$\Rightarrow 2(x + 17) = 3(x + 7) \quad$$[Cross-multiplication]

$$\Rightarrow 2x + 34 = 3x + 21\quad$$[Solving the bracket]

$$\Rightarrow 2x – 3x = 21 – 34 \quad$$[Transposing 3x to LHS and 34 to RHS]

$$\Rightarrow -x = -13$$

$$\Rightarrow x = 13$$

Hence, numerator = 13

and denominator = 13 + 8 = 21

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