Aptitude Question ID : 94726

The value of
\frac{2\frac{1}{3}-1\frac{2}{11}}{3+\frac{1}{3+\frac{1}{3+\frac{1}{3}}}} is :
[A]1
[B]\frac{38}{109}
[C]\frac{109}{38}
[D]\frac{116}{109}

\mathbf{\frac{38}{109}}
Expression = \frac{2\frac{1}{3}-1\frac{2}{11}}{3+\frac{1}{3+\frac{1}{3+\frac{1}{3}}}}
= \frac{\frac{7}{3}-\frac{13}{11}}{3+\frac{1}{3+\frac{1}{\frac{9+1}{3}}}} = \frac{\frac{77-39}{33}}{3+\frac{1}{3+\frac{3}{10}}}
= \frac{\frac{38}{33}}{3+\frac{1}{\frac{30+3}{10}}} = \frac{\frac{38}{33}}{3+\frac{10}{33}}
= \frac{\frac{38}{33}}{\frac{99+10}{33}}
= \frac{38}{33}\times \frac{33}{109} = \frac{38}{109}
Hence option [B] is right answer.

Advertisement

Comments