The sum of the numerator and denominator of a positive fraction

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The sum of the numerator and denominator of a positive fraction is 11. If 2 is added to both numerator and denominator, the fraction is increased by 1/24.The difference of numerator and denominator of the fraction is

1. 5
2. 3
3. 1
4. 9

Correct Option: C

Let numerator be x, then denominator = 11 – x.

∴ Fraction =	x
	11 − x

Again,	x + 2
	11 − x + 2

=	x	+	1
	11 − x		24

⇒	x + 2	+	x	=	1
	13 − x		11 − x		24

⇒	11x − x² + 22 − 2x − 13x + x²	=	1
	(13 − x )(11 − x)		24

⇒ 528 – 96x = 143 – 24x + x²
⇒ x² + 72x – 385 = 0
⇒ x² + 77x – 5x – 385 = 0
⇒ x (x + 77) – 5 (x + 77) = 0
⇒ (x – 5) (x + 77) = 0 ⇒ x = 5
∴ Denominator = 11 – 5 = 6
∴ Difference = 6 – 5 = 1