# Aptitude Question ID : 94821

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

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