Question : Find the value of $\frac{\frac{1}{3} + \frac{1}{4}[\frac{2}{5}-\frac{1}{2}]}{1\frac{2}{3} \text{of} \frac{3}{4}-\frac{3}{4} \text{of} \frac{4}{5}}$.
Option 1: $\frac{37}{78}$
Option 2: $\frac{37}{13}$
Option 3: $\frac{74}{78}$
Option 4: $\frac{74}{13}$
Correct Answer: $\frac{37}{78}$
Solution :
Given: $\frac{\frac{1}{3} + \frac{1}{4}[\frac{2}{5}–\frac{1}{2}]}{1\frac{2}{3} \text{of} \frac{3}{4}–\frac{3}{4} \text{of} \frac{4}{5}}$
Applying the BODMAS rule, we get,
= $\frac{\frac{1}{3}+\frac{1}{4}[\frac{4–5}{10}]}{1\frac{2}{3} \text{of}\frac{3}{4}–\frac{3}{4}\text{of} \frac{4}{5}}$
= $\frac{\frac{1}{3}+\frac{1}{4}[\frac{–1}{10}]}{\frac{5}{3} \text{of}\frac{3}{4}–\frac{3}{4}\text{of}\frac{4}{5}}$
= $\frac{\frac{1}{3}–\frac{1}{40}}{\frac{5}{4}–\frac{3}{5}}$
= $\frac{\frac{40–3}{120}}{\frac{25–12}{20}}$
= $\frac{\frac{37}{120}}{\frac{13}{20}}$
= $\frac{37\times20}{120\times13}$
= $\frac{37}{78}$
Hence, the correct answer is $\frac{37}{78}$.
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