Aptitude Question ID : 94802
Find out the value of
$latex \frac{4\frac{2}{7}-\frac{1}{2}}{3\frac{1}{2}+1\frac{1}{7}}\div \frac{1}{2+\frac{1}{2+\frac{1}{5-\frac{1}{5}}}}&s=2$
[A]$latex 1$
[B]$latex \frac{1}{3}&s=1$
[C]$latex \frac{1}{2}&s=1$
[D]$latex 2$
$latex \mathbf{2}$
$latex First Part = \frac{\frac{30}{7}-\frac{1}{2}}{\frac{7}{2}+\frac{8}{7}}&s=2$
$latex = \frac{\frac{60-7}{14}}{\frac{49+16}{14}} = \frac{53}{14}\times \frac{14}{65} = \frac{53}{65}&s=2$
$latex Second Part = \frac{1}{2+\frac{1}{2+\frac{1}{\frac{25-1}{5}}}}&s=2$
$latex = \frac{1}{2+\frac{1}{2+\frac{5}{24}}} = \frac{1}{2+\frac{1}{\frac{48+5}{24}}}&s=2$
$latex = \frac{1}{2+\frac{24}{53}} = \frac{1}{\frac{106+24}{53}} = \frac{53}{130}&s=2$
$latex \therefore Expression = \frac{53}{65}\div \frac{53}{130}&s=1$
$latex = \frac{53}{65}\times \frac{130}{53} = 2&s=1$
Hence option [D] is right answer.