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Quantitative Aptitude

Simplify:645÷[414÷{513×38+(312+23)×45}]6\frac{4}{5}÷[4\frac{1}{4}÷\{5\frac{1}{3}×\frac{3}{8} + (3\frac{1}{2}+\frac{2}{3})×\frac{4}{5}\}]654÷[441÷{5

Question

Simplify:
$6\frac{4}{5}÷[4\frac{1}{4}÷\{5\frac{1}{3}×\frac{3}{8} + (3\frac{1}{2}+\frac{2}{3})×\frac{4}{5}\}]$

A.

$8\frac{8}{15}$

B.

$7\frac{8}{25}$

C.

$8\frac{8}{25}$

D.

$7\frac{8}{15}$

Solution

Correct option is A

Given:

To find: value of

6\frac{4}{5}÷[4\frac{1}{4}÷\{5\frac{1}{3}×\frac{3}{8} + (3\frac{1}{2}+\frac{2}{3})×\frac{4}{5}\}]

Concept Used:

BODMAS rule:

\begin{array}{|c|c|} \hline \textbf{Operation preference wise} & \textbf{Symbol} \\ \hline Brackets &[],{}, () \\ \hline Orders, of & ² (power), √ (root) , of \\ \hline Division & ÷ \\ \hline Multiplication & × \\ \hline Addition & + \\ \hline Subtraction & - \\ \hline \end{array}

Solution:

6\frac{4}{5}÷[4\frac{1}{4}÷\{5\frac{1}{3}×\frac{3}{8} + (3\frac{1}{2}+\frac{2}{3})×\frac{4}{5}\}]\\\ \\=\frac{34}{5}÷[\frac{17}{4}÷\{\frac{16}{3}×\frac{3}{8} + (\frac{7}{2}+\frac{2}{3})×\frac{4}{5}\}]\\\ \\=\frac{34}{5}÷[\frac{17}{4}÷\{2 + (\frac{25}{6})×\frac{4}{5}\}]\\\ \\=\frac{34}{5}÷[\frac{17}{4}÷\{2 + (\frac{10}{3})]\\\ \\=\frac{34}{5}÷[\frac{17}{4}÷\frac{16}{3}]\\\ \\=\frac{34}{5}÷[\frac{17}{4}×\frac{3}{16}]\\\ \\=\frac{34}{5}÷\frac{51}{64}\\\ \\=\frac{34}{5}× \frac{64}{51} = \frac{128}{15} = 8 \frac{8}{15}

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