The denominator of a rational number is greater than its numerator by 8 if the mumerator is increased by 17 and denominator is decreased by 1 the number obtained is 3/2 find the rational number.
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Suppose numerator of the rational number is p, then denominator is p+8.
Rational number is p+8p.
Numerator is increased by 17, then it becomes p+17.
Denominator is decreased by 1, then it becomes p+8−1=p+7
New rational number is p+7p+17=23
⇒2p+34=3p+21
⇒p=13
Thus numerator is 13.
Denominator is p+8=13+8=21
Therefore, the rational number is 21/13.
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