Answer: Option B
:
B
Conventional Approach
Here we have to compare the ratios 5184/13386, 2318/6049, i.e. we have to compare 51.84% of 6049 and 23.18% of 13386.
50% of 6049 is 3024.5; 1% of 6049 is 60.49; 0.8% of 6049 is 48.392; 0.05% of 6049 is 3.0245. Thus, 51.85% of 6049 is 3024.5 + 60.49 + 48.392 + 3.02 = 3136.4.
Similarly, 20% of 13386 is 2677.2; 3% of 13386 is 401.58; 0.1% of 13386 is 13.386, and 0.08% is 10.708 and thus 23.18% of 13386 is 2677.2 + 401.58 + 13.38 + 10.70 = 3102.86.
Thus, the first ratio is greater and thus OPM of 2000 is greater than that for 1999.
Shortcut
Cut down the number of digits. (OPM)99 $=\frac{13-8}{13}=\frac{5}{13}$ and (OPM)2000 $=\frac{6-3}{3}=\frac{3}{6}$ or $\frac{1}{2}$. Thus you can directly see that $\frac{1}{2}$ is greater than $\frac{5}{13}$.