Aptitude Question ID : 94807

Find out the value of
\sqrt{\frac{4\frac{1}{7}-2\frac{1}{4}}{3\frac{1}{2}+1\frac{1}{7}}\div \frac{1}{2+\frac{1}{2+\frac{1}{5-\frac{1}{5}}}}}
[A]1
[B]2
[C]3
[D]4

1
\frac{4\frac{1}{7}-2\frac{1}{4}}{3\frac{1}{2}+1\frac{1}{7}} = \frac{\frac{29}{7}-\frac{9}{4}}{\frac{7}{2}+\frac{8}{7}}
= \frac{\frac{116-63}{28}}{\frac{49+16}{14}} = \frac{53}{28}\times \frac{14}{65} = \frac{53}{130}
Now, \frac{1}{2+\frac{1}{2+\frac{1}{5-\frac{1}{5}}}}
= \frac{1}{2+\frac{1}{2+\frac{1}{\frac{25-1}{5}}}} = \frac{1}{2+\frac{1}{2+\frac{5}{24}}}
= \frac{1}{2+\frac{1}{\frac{48+5}{24}}} = \frac{1}{2+\frac{24}{53}}
= \frac{1}{\frac{106+24}{53}} = \frac{53}{130}
\therefore Expression = \sqrt{\frac{53}{130} \div \frac{53}{130}} = 1
Hence option [A] is right answer.

Advertisement

Comments