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Anil buys $12$ toys and labels each with the same selling price. He sells $8$ toys initially at $20\%$ discount on the labeled price. Then he sells the remaining $4$ toys at an additional $25\%$ discount on the discounted price. Thus, he gets a total of $\text{Rs }2112,$ and makes a $10\%$ profit. With no discounts, his percentage of profit would have been

1. $60$
2. $55$
3. $50$
4. $54$

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 $: \text{C}$
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