# Aptitude Question ID: 106413

If $\frac{3}{4}$ of the difference of $2\frac{1}{4}$ and $1\frac{2}{3}$ is subtracted from $\frac{2}{3}$ of $3\frac{1}{4}$ the result is :
[A]$\frac{-48}{83}$
[B]$\frac{48}{83}$
[C]$\frac{-83}{48}$
[D]$\frac{83}{48}$

$\mathbf{\frac{83}{48}}$
$\frac{13}{4}\times \frac{2}{3}-\left ( \frac{9}{4}-\frac{5}{3} \right )\times \frac{3}{4}$
$= \frac{13}{6}-\left ( \frac{27-20}{12} \right )\times \frac{3}{4}$
$= \frac{13}{6}-\frac{7}{12}\times \frac{3}{4}$
$= \frac{13}{6}-\frac{7}{16}$
$= \frac{104-21}{48} = \frac{83}{48}$
Hence option [D] is right answer.