# 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.