Anil buys 12 toys and labels each with the same selling price. He sells 8 toys initially at 20% discount on the labelled 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

Options

A. 44.44
B. 54.54
C. 50
D. 60

Answer

To solve the problem step by step, we will break down the information given and perform the necessary calculations.

### Step 1: Define Variables
Let the labeled price of one toy be \( x \).

### Step 2: Calculate Selling Price of 8 Toys
Anil sells 8 toys at a 20% discount. The selling price after the discount is:
\[ \text{Selling Price of 8 toys} = 8 \times \left( x \times \frac{80}{100} \right) = 8 \times \frac{4x}{5} = \frac{32x}{5} \]

### Step 3: Calculate Selling Price of Remaining 4 Toys
The remaining 4 toys are sold at an additional 25% discount on the discounted price. The selling price of one toy after the first discount is \( \frac{4x}{5} \). The new selling price after an additional 25% discount is:
\[ \text{Selling Price of one toy} = \frac{4x}{5} \times \frac{75}{100} = \frac{4x}{5} \times \frac{3}{4} = \frac{3x}{5} \]
Thus, the selling price of 4 toys is:
\[ \text{Selling Price of 4 toys} = 4 \times \frac{3x}{5} = \frac{12x}{5} \]

### Step 4: Total Selling Price
The total selling price for all 12 toys is:
\[ \text{Total Selling Price} = \frac{32x}{5} + \frac{12x}{5} = \frac{44x}{5} \]

### Step 5: Set Up the Equation
According to the problem, the total selling price is Rs 2112. Therefore, we set up the equation:
\[ \frac{44x}{5} = 2112 \]

### Step 6: Solve for \( x \)
To find \( x \), multiply both sides by 5:
\[ 44x = 2112 \times 5 \]
\[ 44x = 10560 \]
Now, divide by 44:
\[ x = \frac{10560}{44} = 240 \]

### Step 7: Calculate Cost Price
Anil makes a 10% profit on the cost price. Let the cost price of 12 toys be \( CP \). The selling price is given as:
\[ SP = CP + 0.1 \times CP = 1.1 \times CP \]
Since the selling price is Rs 2112:
\[ 1.1 \times CP = 2112 \]
Now, solve for \( CP \):
\[ CP = \frac{2112}{1.1} = 1920 \]

### Step 8: Calculate Selling Price Without Discounts
If there were no discounts, the selling price for 12 toys would be:
\[ SP = 12 \times x = 12 \times 240 = 2880 \]

### Step 9: Calculate Profit
The profit when selling without discounts is:
\[ \text{Profit} = SP - CP = 2880 - 1920 = 960 \]

### Step 10: Calculate Profit Percentage
The profit percentage is given by:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{CP} \right) \times 100 = \left( \frac{960}{1920} \right) \times 100 = 50\% \]

### Final Answer
Thus, the percentage of profit with no discounts would have been **50%**.

---