If Fatima sells 60 identical toys at a 40% discount on the printed price, then she makes 20% profit. Ten of these toys are destroyed in fire. While selling the rest, how much discount should be given on the printed price so that she can make the same amount of profit?

Options

A. `30%`
B. `25%`
C. `24%`
D. `28%`

Answer

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

### Step 1: Determine the Printed Price of One Toy
Let's assume the printed price (MP) of one toy is Rs. 100.

**Hint:** You can choose any value for the printed price as long as you maintain the ratio for calculations.

### Step 2: Calculate the Total Printed Price for 60 Toys
The total printed price for 60 toys will be:
\[ \text{Total MP} = \text{MP of one toy} \times \text{Number of toys} = 100 \times 60 = Rs. 6000 \]

**Hint:** Multiply the printed price of one toy by the total number of toys to get the total printed price.

### Step 3: Calculate the Selling Price After Discount
Fatima sells the toys at a 40% discount. Therefore, the selling price (SP) after discount is calculated as follows:
\[ \text{Discount} = 40\% \text{ of } 6000 = \frac{40}{100} \times 6000 = Rs. 2400 \]
\[ \text{Selling Price} = \text{Total MP} - \text{Discount} = 6000 - 2400 = Rs. 3600 \]

**Hint:** To find the selling price after discount, subtract the discount amount from the total printed price.

### Step 4: Calculate the Cost Price of One Toy
Fatima makes a 20% profit on the selling price. Thus, we can find the cost price (CP) using the formula:
\[ \text{Selling Price} = \text{Cost Price} + \text{Profit} \]
Since profit is 20% of CP, we can express this as:
\[ 3600 = CP + 0.2 \times CP = 1.2 \times CP \]
Now, rearranging gives:
\[ CP = \frac{3600}{1.2} = Rs. 3000 \]

**Hint:** Use the relationship between selling price, cost price, and profit to find the cost price.

### Step 5: Calculate the Cost Price of One Toy
To find the cost price of one toy:
\[ \text{Cost Price of One Toy} = \frac{3000}{60} = Rs. 50 \]

**Hint:** Divide the total cost price by the number of toys to find the cost price per toy.

### Step 6: Calculate the Selling Price for Remaining Toys
Since 10 toys are destroyed, the remaining toys are:
\[ \text{Remaining Toys} = 60 - 10 = 50 \]
The total cost price for these 50 toys is:
\[ \text{Total CP for 50 Toys} = 50 \times 50 = Rs. 2500 \]

**Hint:** Subtract the destroyed toys from the total to find the remaining toys.

### Step 7: Calculate the Required Selling Price to Maintain Profit
To maintain the same profit of Rs. 600 (which is Rs. 3600 - Rs. 3000), the selling price for the 50 toys must be:
\[ \text{Required Selling Price} = \text{Total CP} + \text{Profit} = 2500 + 600 = Rs. 3100 \]

**Hint:** Add the desired profit to the total cost price of the remaining toys to find the required selling price.

### Step 8: Calculate the Discount Required on the Printed Price
The printed price for 50 toys is:
\[ \text{Total MP for 50 Toys} = 100 \times 50 = Rs. 5000 \]
Now, the discount needed to achieve the required selling price is:
\[ \text{Discount} = \text{Total MP} - \text{Required Selling Price} = 5000 - 3100 = Rs. 1900 \]

**Hint:** Subtract the required selling price from the total printed price to find the discount.

### Step 9: Calculate the Percentage of Discount
The percentage of discount on the printed price is:
\[ \text{Discount Percentage} = \left(\frac{1900}{5000}\right) \times 100 = 38\% \]

**Hint:** To find the percentage, divide the discount by the total printed price and multiply by 100.

### Final Answer
Fatima should give a discount of **38%** on the printed price to maintain the same profit.