RRB Technician Grade I 19 Dec 2024 Shift 1 Paper

Concept:Use BODMAS and simplify the bracket before performing division.Explanation:The given expression is:$$\frac{1}{(\frac{5}{6})+(\frac{2}{4})}\div \frac{4}{29}$$First, solve the denominator inside the bracket.$$\frac{5}{6}+\frac{2}{4}$$LCM of $6$ and $4$ is $12$.$$=\frac{5\times 2+2\times 3}{12}=\frac{10+6}{12}=\frac{16}{12}$$Simplify the fraction:$$\frac{16}{12}=\frac{4}{3}$$Substitute back into the main expression:$$\frac{1}{\frac{4}{3}}\div \frac{4}{29}$$$$\frac{3}{4}\div \frac{4}{29}$$Change division to multiplication by taking the reciprocal:$$\frac{3}{4}\times \frac{29}{4}$$$$=\frac{87}{16}$$Convert to a mixed fraction:$87 \div 16 = 5$ with remainder $7$, so:$$\frac{87}{16}=5\frac{7}{16}$$Answer:The correct answer is option B: $5\frac{7}{16}$.