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.

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