Aptitude Question ID : 94830

The value of
4-\frac{1}{1+\frac{1}{3+\frac{1}{2+\frac{1}{4}}}} is :
[A]\frac{1}{64}
[B]\frac{1}{32}
[C]\frac{1}{16}
[D]\frac{1}{8}

\mathbf{\frac{1}{8}}
Expression = 4-\frac{5}{1+\frac{1}{3+\frac{1}{\frac{8+1}{4}}}}
= 4-\frac{5}{1+\frac{1}{3+\frac{4}{9}}} = 4-\frac{5}{1+\frac{1}{\frac{27+4}{9}}}
= 4-\frac{5}{1+\frac{9}{31}} = 4-\frac{5}{\frac{31+9}{31}}
= 4-\frac{5\times 31}{40} = \frac{160-155}{40}
= \frac{5}{40} = \frac{1}{8}
Hence option [D] is right answer.

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