Aptitude Question ID : 94726
The value of
$latex \frac{2\frac{1}{3}-1\frac{2}{11}}{3+\frac{1}{3+\frac{1}{3+\frac{1}{3}}}}&s=2$ is :
[A]$latex 1$
[B]$latex \frac{38}{109}&s=1$
[C]$latex \frac{109}{38}&s=1$
[D]$latex \frac{116}{109}&s=1$
$latex \mathbf{\frac{38}{109}}&s=1$
$latex Expression = \frac{2\frac{1}{3}-1\frac{2}{11}}{3+\frac{1}{3+\frac{1}{3+\frac{1}{3}}}}&s=2$
$latex = \frac{\frac{7}{3}-\frac{13}{11}}{3+\frac{1}{3+\frac{1}{\frac{9+1}{3}}}} = \frac{\frac{77-39}{33}}{3+\frac{1}{3+\frac{3}{10}}}&s=2$
$latex = \frac{\frac{38}{33}}{3+\frac{1}{\frac{30+3}{10}}} = \frac{\frac{38}{33}}{3+\frac{10}{33}}&s=2$
$latex = \frac{\frac{38}{33}}{\frac{99+10}{33}}&s=2$
$latex = \frac{38}{33}\times \frac{33}{109} = \frac{38}{109}&s=1$
Hence option [B] is right answer.