RRB Technician Grade I 20 Dec 2024 Shift 1 Paper

Concept:Use fraction addition and division by reciprocal to evaluate the expression.Explanation:First, simplify the fraction inside the denominator.$\frac{4}{6} = \frac{2}{3}$So the expression becomes:$\left(\frac{1}{\frac{3}{4} + \frac{2}{3}}\right) \div \frac{2}{15}$Add the fractions in the denominator:$\frac{3}{4} + \frac{2}{3} = \frac{9 + 8}{12} = \frac{17}{12}$Now the expression is:$\frac{1}{\frac{17}{12}} \div \frac{2}{15}$Simplify $\frac{1}{\frac{17}{12}} = \frac{12}{17}$Then divide by $\frac{2}{15}$ by multiplying with its reciprocal:$\frac{12}{17} \div \frac{2}{15} = \frac{12}{17} \times \frac{15}{2}$$= \frac{180}{34} = \frac{90}{17}$Convert the improper fraction to a mixed fraction:$\frac{90}{17} = 5\frac{5}{17}$Answer:$5\frac{5}{17}$So, the correct option is A.