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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 \( \Large \frac{1}{24} \). The differ-ence of numerator and den-ominator of the fraction is:

A) 5
B) 3
C) 1
D) 9

Correct Answer:



C) 1

Description for Correct answer:
Let the numerator and denominator be \( \Large\textit{x}\)and 11 - \( \Large\textit{x}\)

According to question

fraction \( \Large =\frac{x}{11-x} \)

\( \Large \frac{x+2}{11-x+2}=\frac{x}{11-x}\frac{1}{24} \)

\( \Large \frac{x+2}{13-x}-\frac{x}{11-x}=\frac{1}{24} \)

\( \Large \frac{11x+22-x^{2}-2x-13x+x^{2}}{(13-x)(11-x)}=\frac{1}{24} \)

\( \Large 528-96x=143-24x+x^{2} \)

\( \Large x^{2}+72x-385=0 \)

\( \Large (x+77)(x-5)=0 \)

\( \Large x=5 \)

Numerator (x) = 5

Denominator = 11 - 5 = 6

Difference = 6 - 5 = 1

Part of solved Number series questions and answers : >> Aptitude >> Number series

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