Solve : $$7\frac{1}{2} - $$ $$\left[ {2\frac{1}{4} ÷ \left\{ {1\frac{1}{4} - \frac{1}{2}\left( {1\frac{1}{2} - \frac{1}{3} - \frac{1}{6}} \right)} \right\}} \right]$$ = ?
A. $$\frac{2}{9}$$
B. $$4\frac{1}{2}$$
C. $$9\frac{1}{2}$$
D. $$1\frac{77}{228}$$
Answer: Option B
Solution(By Examveda Team)
$$ = 7\frac{1}{2} - $$ $$\left[ {2\frac{1}{4} \div \left\{ {1\frac{1}{4} - \frac{1}{2}\left( {1\frac{1}{2} - \frac{1}{3} - \frac{1}{6}} \right)} \right\}} \right]$$$$ = \frac{{15}}{2} - $$ $$\left[ {\frac{9}{4} \div \left\{ {\frac{5}{4} - \frac{1}{2}\left( {\frac{3}{2} - \frac{1}{3} - \frac{1}{6}} \right)} \right\}} \right]$$
$$ = \frac{{15}}{2} - $$ $$\left[ {\frac{9}{4} \div \left\{ {\frac{5}{4} - \frac{1}{2}\left( {\frac{{9 - 2 - 1}}{6}} \right)} \right\}} \right]$$
$$\eqalign{ & = \frac{{15}}{2} - \left[ {\frac{9}{4} \div \left\{ {\frac{5}{4} - \frac{1}{2}} \right\}} \right] \cr & = \frac{{15}}{2} - \left[ {\frac{9}{4} \div \left\{ {\frac{{5 - 2}}{4}} \right\}} \right] \cr & = \frac{{15}}{2} - \left[ {\frac{9}{4} \div \frac{3}{4}} \right] \cr & = \frac{{15}}{2} - \left[ {\frac{9}{4} \times \frac{4}{3}} \right] \cr & = \frac{{15}}{2} - 3 \cr & = \frac{{15 - 6}}{2} \cr & = \frac{9}{2} \cr & = 4\frac{1}{2} \cr} $$
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