Question : The value of $\left[1 \frac{2}{7} \times\left\{3 \frac{1}{2} \div\left(\frac{1}{2}-\frac{1}{7}\right)\right\}\right] \div\left(4 \frac{1}{5} \times 1 \frac{1}{2}\right)$ is:
Option 1: $\frac{1}{3}$
Option 2: $\frac{3}{4}$
Option 3: $2$
Option 4: $1$
Correct Answer: $2$
Solution :
Given: $\left[1 \frac{2}{7} \times\left\{3 \frac{1}{2} \div\left(\frac{1}{2}-\frac{1}{7}\right)\right\}\right] \div\left(4 \frac{1}{5} \times 1 \frac{1}{2}\right)$
= $\left[\frac{9}{7} \times\left\{\frac{7}{2} \div\left(\frac{7-2}{14}\right)\right\}\right] \div\left( \frac{21}{5} \times \frac{3}{2}\right)$
= $\left[\frac{9}{7} \times\left\{\frac{7}{2} \div\frac{5}{14}\right\}\right] \div\left( \frac{21}{5} \times \frac{3}{2}\right)$
= $\left[\frac{9}{7} \times\left\{\frac{7}{2} \times\frac{14}{5}\right\}\right] \div\left( \frac{63}{10}\right)$
= $\left[\frac{9}{7} \times\left\{\frac{98}{10} \right\}\right] \div\left( \frac{63}{10}\right)$
= $\frac{9}{7} \times\frac{98}{10} \times\frac{10}{63}$
= $2$
Hence, the correct answer is 2.
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