Simplify the following expression. (\frac{3}{4}-\frac{1}{4} \div \frac{1}{4} of \frac{2}{5}) \div(\frac{3}{4} \div \frac{2}{3} of \frac{3}{5})

SSC CGL 24 Aug 2021 Shift 3 Paper

Question : 70 of 100

Marks: +1, -0

Simplify the following expression.

(\;{3}/{4}-\;{1}/{4} ÷ \;{1}/{4}

\;{2}/{5}) ÷(\;{3}/{4} ÷ \;{2}/{3}

\;{3}/{5})

Solution:

Given expression,

\;\; =[\;{3}/{4}-\;{1}/{4} ÷ \;{1}/{4} \;\text " of "\; \;{2}/{5}] ÷[\;{3}/{4} ÷ \;{2}/{3} \;\text " of "\; \;{3}/{5}]

\;\; =[\;{3}/{4}-\;{1}/{4} ÷(\;{1}/{4} × \;{2}/{5})] ÷[\;{3}/{4} ÷(\;{2}/{3} × \;{3}/{5})]

\;\; =[\;{3}/{4}-(\;{1}/{4} ÷ \;{1}/{10})] ÷[\;{3}/{4} ÷ \;{2}/{5}]

\;\; =[\;{3}/{4}-\;{1}/{4} × 10] ÷[\;{3}/{4} × \;{5}/{2}]

=[\;{3}/{4}-\;{5}/{2}] ÷[\;{15}/{8}]=[\;{(3-10)}/{4} × \;{8}/{15}]

=\;{-7}/{4} × \;{8}/{15}=-\;{14}/{15} .

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