Aptitude Question ID : 94821

On simplification, the expression
\frac{4\frac{1}{7}-2\frac{1}{7}}{3\frac{1}{2}+1\frac{1}{7}}\div \frac{1}{2+\frac{1}{2+\frac{1}{5-\frac{1}{5}}}} is equal to :
[A]\frac{14}{65}
[B]\frac{24}{53}
[C]\frac{28}{65}
[D]\frac{56}{53}

\mathbf{\frac{56}{53}}
First Part = \frac{4\frac{1}{7}-2\frac{1}{7}}{3\frac{1}{2}+1\frac{1}{7}}
=\frac{\frac{29}{7}-\frac{15}{7}}{\frac{7}{2}+\frac{8}{7}} = \frac{\frac{14}{7}}{\frac{49+16}{14}}
= \frac{2}{\frac{65}{14}} = \frac{2\times14}{65} = \frac{28}{65}
Second Part = \frac{1}{2+\frac{1}{2+\frac{1}{\frac{25-1}{5}}}}
= \frac{1}{2+\frac{1}{2+\frac{5}{24}}} = \frac{1}{2+\frac{1}{\frac{48+5}{24}}}
= \frac{1}{2+\frac{24}{53}} = \frac{1}{\frac{106+24}{53}} = \frac{53}{130}
\therefore Expression = \frac{28}{65}\div \frac{53}{130}
= \frac{28}{65}\times \frac{130}{53} = \frac{56}{53}
Hence option [D] is right answer.

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