Question : Find the value of the given expression.
$\left(2 \frac{1}{2}÷ 1 \frac{7}{8}\right) ÷\left(9 \frac{3}{8}÷ 11 \frac{2}{3} \text { of } \frac{1}{8}\right)$
Option 1: $\frac{33}{135}$
Option 2: $\frac{11}{135}$
Option 3: $\frac{28}{135}$
Option 4: $\frac{57}{135}$
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Correct Answer: $\frac{28}{135}$
Solution :
Consider, $\left(2 \frac{1}{2}÷ 1 \frac{7}{8}\right) ÷\left(9 \frac{3}{8}÷ 11 \frac{2}{3} \text { of } \frac{1}{8}\right)$
= $(\frac{5}{2}÷\frac{15}{8})÷\{\frac{75}{8}÷(\frac{35}{3}\times\frac{1}{8})\}$
= $(\frac{5}{2}\times\frac{8}{15})÷(\frac{75}{8}\times\frac{3}{35}\times\frac81)$
= $(\frac{4}{3})÷(\frac{15\times 3}{ 7})$
= $(\frac{4}{3})÷(\frac{15\times 3}{ 7})$
= $\frac{4}{3}\times\frac{7}{15\times 3}$
= $\frac{28}{135}$
Hence, the correct answer is $\frac{28}{135}$.
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