Aptitude Question ID : 94704

Simplify :
\left [ \left ( 1+\frac{1}{10+\frac{1}{10}} \right )\times \left ( 1+\frac{1}{10+\frac{1}{10}} \right )- \left ( 1-\frac{1}{10+\frac{1}{10}} \right )\times \left ( 1-\frac{1}{10+\frac{1}{10}} \right ) \right ]\div \left [ \left ( 1+\frac{1}{10+\frac{1}{10}} \right )+\left ( 1-\frac{1}{10+\frac{1}{10}} \right ) \right ]
[A]\frac{101}{100}
[B]\frac{20}{101}
[C]\frac{100}{101}
[D]\frac{90}{101}

\mathbf{\frac{20}{101}}
Suppose that,
1+\frac{1}{10+\frac{1}{10}} = \frac{111}{101} = a
and, 1-\frac{1}{10+\frac{1}{10}} = \frac{91}{101} = b
\therefore \frac{a^{2}-b^{2}}{(a+b)} = \frac{(a+b)(a-b)}{(a+b)}
= (a-b)
= \frac{111}{101} - \frac{91}{101} = \frac{20}{101}
Hence option [B] is right answer.

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