Aptitude Question ID : 94713

Simplify :
\frac{2}{2+\frac{2\times 0.39}{3+\frac{2}{3+\frac{2}{3}}}}
[A]2
[B]6
[C]\frac{100}{111}
[D]\frac{1}{3}

\mathbf{\frac{100}{111}}
Given Expression,
= \frac{2}{2+\frac{2\times 0.39}{3+\frac{2}{3+\frac{2}{3}}}}
= \frac{2}{2+\frac{2\times 0.39}{3+\frac{2}{\frac{11}{3}}}}
= \frac{2}{2+\frac{2\times 0.39}{3+\frac{6}{11}}}
= \frac{2}{2+\frac{2\times 0.39}{\frac{33+6}{11}}}
= \frac{2}{2+\frac{11\times 2\times 0.39}{39}}
= \frac{2}{2+\frac{11\times 2}{39}\times \frac{39}{100}}
= \frac{2}{2+\frac{11}{50}} = \frac{2}{\frac{100+11}{50}}
= \frac{100}{111}
Hence option [C] is right answer.

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