Question : What is the value of $\frac{\left[\left(\frac{5}{7} \text { of } \frac{1}{12} \times \frac{1}{4}-\frac{1}{2} \times \frac{1}{8}\right)+\frac{5}{4} \times \frac{8}{15}-\frac{2}{3}\right]}{\frac{1}{2} \div \frac{1}{4}+\frac{1}{2}}$ ?
Option 1: $\frac{-5}{108}$
Option 2: $\frac{-4}{103}$
Option 3: $\frac{-4}{105}$
Option 4: $\frac{-2}{105}$
Correct Answer: $\frac{-2}{105}$
Solution :
$\frac{\left[\left(\frac{5}{7} \text { of } \frac{1}{12} \times \frac{1}{4}-\frac{1}{2} \times \frac{1}{8}\right)+\frac{5}{4} \times \frac{8}{15}-\frac{2}{3}\right]}{\frac{1}{2} \div \frac{1}{4}+\frac{1}{2}}$
= $\frac{\left[\left(\frac{5}{336} -\frac{1}{16} \right) + \frac{2}{3} \ -\frac{2}{3}\right]}{\frac{1}{2} \div \frac{1}{4}+\frac{1}{2}}$ = $\frac{\left[\left(\frac{5}{336} -\frac{1}{16} \right) + \frac{2}{3} \ -\frac{2}{3}\right]}{{2} +\frac{1}{2}}$ = $\frac{\frac{5 – 21}{336}}{\frac{5}{2}}$ = $\frac{\frac{-16}{336}}{\frac{5}{2}}$ = – $\frac{2}{105}$
Hence, the correct answer is – $\frac{2}{105}$.
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