In place of `18%` profit an article is sold at `42%` profit and seller gets 110.40 more find selling price of article if it was sold at 25% profit

Options

A. `₹440`
B. `₹460`
C. `₹575`
D. `₹550`

Answer

To solve the problem step by step, we will follow the logic outlined in the video transcript.

### Step 1: Define the Cost Price
Let the cost price (CP) of the article be \( x \) rupees.

### Step 2: Calculate Selling Prices at Different Profits
1. **Selling Price at 18% Profit**:
\[ SP_1 = CP + 18\% \text{ of } CP = x + \frac{18}{100}x = \frac{118}{100}x = \frac{59}{50}x \]

2. **Selling Price at 42% Profit**:
\[ SP_2 = CP + 42\% \text{ of } CP = x + \frac{42}{100}x = \frac{142}{100}x = \frac{71}{50}x \]

### Step 3: Set Up the Equation Based on the Given Information
According to the problem, the difference between the selling prices at 42% and 18% profit is \( 110.40 \) rupees:
\[ SP_2 - SP_1 = 110.40 \]
Substituting the values we calculated:
\[ \frac{71}{50}x - \frac{59}{50}x = 110.40 \]
This simplifies to:
\[ \frac{12}{50}x = 110.40 \]

### Step 4: Solve for the Cost Price \( x \)
To eliminate the fraction, multiply both sides by \( 50 \):
\[ 12x = 110.40 \times 50 \]
Calculating the right side:
\[ 12x = 5520 \]
Now, divide by 12:
\[ x = \frac{5520}{12} = 460 \]

### Step 5: Calculate the Selling Price at 25% Profit
Now we need to find the selling price if the article was sold at 25% profit:
\[ SP_3 = CP + 25\% \text{ of } CP = x + \frac{25}{100}x = \frac{125}{100}x = \frac{5}{4}x \]
Substituting \( x = 460 \):
\[ SP_3 = \frac{5}{4} \times 460 = 575 \]

### Final Answer
The selling price of the article if it was sold at 25% profit is **575 rupees**.

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