# Aptitude Question ID : 94694

Find out the value of $2x+\frac{7}{4}$, if
$x= 1 +\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{1}{2}}}}$
[A]3
[B]4
[C]5
[D]6

5
Given that
$x= 1 +\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{1}{2}}}}$
$= 1+\frac{1}{1+\frac{1}{1+\frac{1}{\frac{3}{2}}}} = 1+\frac{1}{1+\frac{1}{1+\frac{2}{3}}}$
$= 1+\frac{1}{1+\frac{1}{\frac{5}{3}}} = 1+\frac{1}{1+\frac{3}{5}}$
$= 1+\frac{1}{\frac{8}{5}} = 1+\frac{5}{8} = \frac{13}{8}$
$\therefore 2x + \frac{7}{4} = 2\times \frac{13}{8}+\frac{7}{4}$
$= \frac{13+7}{4} = \frac{20}{4} = 5$
Hence option [C] is right answer.