Let the cost price and marked price of each toy be $\text{c}$ and $\text{m},$ respectively.
Overall selling price $ = 8 (0.8 \; \text{m}) + 4 \left( \frac{3}{4} \times 0.8 \; \text{m} \right) = 6.4 \; \text{m} + 2.4 \; \text{m} = 8.8 \; \text{m}$
Now, $110 \% \; \text{of} \;12 \; \text{c} = 8.8 \; \text{m}$
$\Rightarrow \frac{110}{100} \times 12 \; \text{c} = 8.8 \; \text{m}$
$\Rightarrow \boxed{3 \; \text{c} = 2 \; \text{m}}$
Overall cost price $ = 12 \times \text{c}= 12 \times \frac{2 \; \text{m}}{3}= 8 \; \text{m}$
$\therefore$ Required profit percentage $ = \left( \frac{12 \; \text{m} – 8 \; \text{m}}{8 \; \text{m}} \right) \times 100 \% = \frac{4 \; \text{m}}{8 \; \text{m}} \times 100 \% = 50 \%.$
Correct Answer $: \text{C}$