RRB Technician Grade I 19 Dec 2024 Shift 3 Paper

Concept:Use BODMAS rule and fraction arithmetic. Simplify the bracket first, then divide by multiplying with the reciprocal.Explanation:Start with the expression: $\frac{1}{\left(\frac{5}{6}+\frac{7}{9}\right)}\div \frac{5}{23}$First, solve the bracket. LCM of $6$ and $9$ is $18$.$\frac{5}{6}+\frac{7}{9}=\frac{5\times3+7\times2}{18}=\frac{15+14}{18}=\frac{29}{18}$Now the expression becomes: $\frac{1}{\frac{29}{18}}\div \frac{5}{23}$$\frac{1}{\frac{29}{18}}=\frac{18}{29}$So, $\frac{18}{29}\div \frac{5}{23}$Division means multiply by the reciprocal: $\frac{18}{29}\times \frac{23}{5}$Multiply numerators and denominators: $\frac{18\times23}{29\times5}=\frac{414}{145}$Convert $\frac{414}{145}$ to a mixed fraction: $414\div145=2$ with remainder $124$Thus, $\frac{414}{145}=2\frac{124}{145}$Answer:$2\frac{124}{145}$, which is option A.