There would be 15% loss if a toy is sold for Rs 25.50. At what price should it be sold to earn a profit of 25%?

Options

A. 33.5
B. 35
C. 37.5
D. 36

Answer

To solve the problem step by step, we will follow the reasoning laid out in the video transcript.

### Step 1: Understand the Problem
We have a toy that incurs a 15% loss when sold for Rs 25.50. We need to find the selling price that would yield a 25% profit.

### Step 2: Define the Cost Price
Let the cost price (CP) of the toy be represented as \( X \).

### Step 3: Calculate the Selling Price at 15% Loss
If there is a 15% loss, the selling price (SP) can be expressed as:
\[ SP = CP - \text{Loss} \]
The loss can be calculated as:
\[ \text{Loss} = 15\% \text{ of } CP = \frac{15}{100} \times X = \frac{3X}{20} \]
Thus, the selling price becomes:
\[ SP = X - \frac{3X}{20} \]
To simplify this, we can find a common denominator:
\[ SP = \frac{20X}{20} - \frac{3X}{20} = \frac{17X}{20} \]

### Step 4: Set Up the Equation
According to the problem, when the toy is sold for Rs 25.50, this is equal to the selling price we calculated:
\[ \frac{17X}{20} = 25.50 \]

### Step 5: Solve for Cost Price (X)
To find \( X \), we can rearrange the equation:
\[ 17X = 25.50 \times 20 \]
Calculating the right side:
\[ 17X = 510 \]
Now, divide both sides by 17:
\[ X = \frac{510}{17} = 30 \]
So, the cost price of the toy is Rs 30.

### Step 6: Calculate Selling Price for 25% Profit
To find the selling price for a 25% profit, we first calculate the profit:
\[ \text{Profit} = 25\% \text{ of } CP = \frac{25}{100} \times 30 = 7.5 \]
Now, the selling price for a 25% profit is:
\[ SP = CP + \text{Profit} = 30 + 7.5 = 37.5 \]

### Final Answer
The toy should be sold for Rs 37.5 to earn a profit of 25%.

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