Question : A student was asked to find the value of $\left[(\frac{4}{9} \div \frac{3}{5} \div \frac{3}{2}) \times \frac{9}{25}\right] ×{\left[\frac{2}{3} \text { of } \frac{4}{9} \div\left(3 \times \frac{3}{5} \text { of } \frac{4}{5}\right)\right]}{\frac{2}{3} \div \frac{3}{4} \text { of } 6}$ His answer was $\frac{2}{9}$.
What is the difference between his answer and the correct answer?
Option 1: $\frac{1}{12}$
Option 2: $\frac{1}{4}$
Option 3: $\frac{1}{24}$
Option 4: $\frac{1}{6}$
Correct Answer: $\frac{1}{12}$
Solution :
According to the question
$\left[(\frac{4}{9} \div \frac{3}{5} \div \frac{3}{2}) \times \frac{9}{25}\right] ×{\left[\frac{2}{3} \text { of } \frac{4}{9} \div\left(3 \times \frac{3}{5} \text { of } \frac{4}{5}\right)\right]}{\frac{2}{3} \div \frac{3}{4} \text { of } 6}$
= $\left[(\frac{4}{9} × \frac{5}{3} × \frac{2}{3}) \times \frac{9}{25}\right] ×{\left[\frac{2}{3} \text { of } \frac{4}{9} \div\left(3 \times \frac{3}{5} \text { of } \frac{4}{5}\right)\right]}{\frac{2}{3} \div \frac{3}{4} \text { of } 6}$
= $\frac{8}{45}×{\left[\frac{8}{27} \div\left(\frac{36}{25}\right)\right]}{\frac{2}{3} \div \frac{9}{2}}$
= $\frac{8}{45}×{\left[\frac{8}{27} \div\left(\frac{36}{25}\right)\right]}{\frac{4}{27}}$
= $\frac{8}{45} × \frac{8}{27} × \frac{25}{36} ×\frac{4}{27}$
Now,
Difference = $\frac{25}{324}$ and $\frac{2}{9}$ = $\frac{2}{9}$ – $\frac{25}{324}$
= $\frac{72 - 25}{324}$
= $\frac{47}{324}$
Hence, the correct answer is $\frac{47}{324}$
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