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    Simplify the following expression. ​[8534×118−((4669÷27135)−(86129×9114)) of 11236]\left[ \frac{85}{34} \times \frac{1}{18} - \left( \left(
    Question

    Simplify the following expression.

    ​[8534×118−((4669÷27135)−(86129×9114)) of 11236]\left[ \frac{85}{34} \times \frac{1}{18} - \left( \left( \frac{46}{69} \div \frac{27}{135} \right) - \left( \frac{86}{129} \times \frac{91}{14} \right) \right) \text{ of } \frac{112}{36} \right]​​

    A.

    3.2

    B.

    3.75

    C.

    3.5

    D.

    3.25

    Correct option is D

    Concept Used: 
    BODMAS rule: 
    ​Operation preference wiseSymbolBrackets[],,()Orders, of²(power),√(root),ofDivision÷ Multiplication×Addition+Subtraction−\begin{array}{|c|c|} \hline \textbf{Operation preference wise} & \textbf{Symbol} \\ \hline \text{Brackets} &[],{}, () \\ \hline \text{Orders, of} & ² (power), √ (root) , of \\ \hline \text{Division} & ÷ \\ \hline\text{ Multiplication} & × \\ \hline \text{Addition} & + \\ \hline \text{Subtraction} & - \\ \hline \end{array} ​​
    Solution: 
    =[8534×118−((4669÷27135)−(86129×9114)) of 11236]=52×118−((4669×13527)−(23×132)) of 289=536−(23×5−133) of 289=536+1 of 289=5+11236=11736=134=314=3.25\begin{align*}&=\left[ \frac{85}{34} \times \frac{1}{18} - \left( \left( \frac{46}{69} \div \frac{27}{135} \right) - \left( \frac{86}{129} \times \frac{91}{14} \right) \right) \text{ of } \frac{112}{36} \right]\\&= \frac{5}{2} \times \frac{1}{18} - \left( \left( \frac{46}{69} \times \frac{135}{27} \right) - \left( \frac{2}{3} \times \frac{13}{2} \right) \right) \text{ of } \frac{28}{9} \\&= \frac{5}{36} - \left( \frac{2}{3} \times 5 - \frac{13}{3} \right) \text{ of } \frac{28}{9} \\&= \frac{5}{36} + 1 \text{ of } \frac{28}{9} \\&= \frac{5 + 112}{36} \\&= \frac{117}{36} \\&= \frac{13}{4} = 3 \frac{1}{4} = \bf3.25\end{align*}​​​​

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