Find the value of the following expression.
$$\frac{{1\frac{2}{3} \div \frac{5}{6} \times 6 + \frac{4}{5} \times \frac{1}{2} + \frac{2}{3}}}{{2 - \left[ {1\frac{1}{3} \times \left( { - \frac{3}{5}} \right) - 6\left\{ {\frac{3}{5} - \left( {3 - \frac{3}{{10}}} \right)} \right\}} \right]}}$$
A. $$ - \frac{4}{3}$$
B. $$\frac{4}{3}$$
C. $$\frac{1}{7}$$
D. $$ - \frac{1}{7}$$
Answer: Option A
Solution(By Examveda Team)
$$\eqalign{ & \frac{{1\frac{2}{3} \div \frac{5}{6} \times 6 + \frac{4}{5} \times \frac{1}{2} + \frac{2}{3}}}{{2 - \left[ {1\frac{1}{3} \times \left( { - \frac{3}{5}} \right) - 6\left\{ {\frac{3}{5} - \left( {3 - \frac{3}{{10}}} \right)} \right\}} \right]}} \cr & = \frac{{\frac{5}{3} \times \frac{6}{5} \times 6 + \frac{4}{{10}} + \frac{2}{3}}}{{2 - \left[ {\frac{4}{3} \times \frac{{ - 3}}{5} - 6\left\{ {\frac{3}{5} - \frac{{27}}{{10}}} \right\}} \right]}} \cr & = \frac{{12 + \frac{{6 + 10}}{{15}}}}{{2 - \left( { - \frac{4}{5} + \frac{{21 \times 6}}{{10}}} \right)}} \cr & = \frac{{12 + \frac{{16}}{{15}}}}{{2 - \left( { - \frac{4}{5} + \frac{{63}}{5}} \right)}} \cr & = \frac{{\frac{{196}}{{15}}}}{{2 - \frac{{59}}{5}}} \cr & = \frac{{196}}{{15}} \times \frac{{ - 5}}{{49}} \cr & = \boxed{ - \frac{4}{3}} \cr} $$Related Questions on Simplification
A. 20
B. 80
C. 100
D. 200
E. None of these
A. Rs. 3500
B. Rs. 3750
C. Rs. 3840
D. Rs. 3900
E. None of these
Join The Discussion