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 Rs 2112, and makes a 10% profit. With no discounts, his percentage of profit would have been

The correct answer is 50%.

Let's work through this problem step-by-step, carefully tracking the labeled price, actual revenues, and cost price.

Step 1: Define the Variable
Let the labeled (marked) selling price of each toy = L (in Rs).

Step 2: Calculate Revenue from the First Batch (8 toys at 20% discount)
A 20% discount on the labeled price means each toy is sold at 80% of L.

$$\text{Price per toy (1st batch)}=L\times \frac{80}{100}=0.8L$$

$$\text{Revenue from 8 toys}=8\times 0.8L=6.4L$$

Step 3: Calculate Revenue from the Second Batch (4 toys at an additional 25% discount)
The additional 25% discount is applied on the already discounted price of 0.8L (not on the original labeled price).

$$\text{Price per toy (2nd batch)}=0.8L\times \frac{75}{100}=0.6L$$

$$\text{Revenue from 4 toys}=4\times 0.6L=2.4L$$

Step 4: Find the Labeled Price (L) Using Total Revenue
Total revenue from all 12 toys = Rs 2112.

$$6.4L+2.4L=2112$$

$$8.8L=2112$$

$$L=\frac{2112}{8.8}=240$$

So, the labeled price per toy = Rs 240.

Step 5: Find the Total Cost Price Using the 10% Profit Condition
Anil makes a 10% profit on the total revenue of Rs 2112. This means:

$$\text{Total Revenue}=\text{Cost Price}\times \frac{110}{100}$$

$$2112=\text{CP}\times 1.1$$

$$\text{CP}=\frac{2112}{1.1}=\mathrm{Rs}1920$$

So, the total cost price of all 12 toys = Rs 1920.

Step 6: Calculate the Revenue WITHOUT Any Discounts
If Anil sells all 12 toys at the full labeled price of Rs 240 each:

$$\text{Total Revenue (no discount)}=12\times 240=\mathrm{Rs}2880$$

Step 7: Calculate the Profit Percentage WITHOUT Discounts

$$\text{Profit (no discount)}=2880-1920=\mathrm{Rs}960$$

$$\text{Profit \%}=\frac{\text{Profit}}{\text{Cost Price}}\times 100=\frac{960}{1920}\times 100=50\%$$

Conclusion:
If Anil had sold all 12 toys at the labeled price with no discounts, he would have made a profit of 50%. This confirms that the correct answer is 50.