Correct Answer: $30\frac{5}{8}\%$

Solution : Let the cost of production as $C$ and the selling price as $S$.
Given that the manufacturer fixes his selling price at 33% over the cost of production,
$S = C + 0.33C = 1.33C$
The cost of production goes up by 12%, the new cost of production,
$C' = C + 0.12C = 1.12C$
The manufacturer raises his selling price by 10%, the new selling price,
$S' = S + 0.10S = 1.10S$
$S' = 1.10 \times 1.33C = 1.463C$
$\text{Profit Percentage} = \frac{S' - C'}{C'} \times 100$
$\text{Profit Percentage} = \frac{1.463C - 1.12C}{1.12C} \times 100 = \frac{0.343C}{1.12C} \times 100=30\frac{5}{8}\%$
Hence, the correct answer is $30\frac{5}{8}\%$.