In place of 18% profit an article is sold at 32% profit and seller gets ₹112 more. Fmd the selling price of article ifitwere sold at 25% profit?

Options

A. ₹440
B. ₹460
C. ₹1000
D. ₹ 550

Explanation

To solve the problem, we will follow these steps:

### Step 1: Define Variables
Let the cost price (CP) of the article be ₹x.

### Step 2: Calculate Selling Prices
1. Selling Price (SP) at 18% profit:
\[ SP_{18\%} = CP + 18\% \text{ of } CP = x + 0.18x = 1.18x \]

2. Selling Price (SP) at 32% profit:
\[ SP_{32\%} = CP + 32\% \text{ of } CP = x + 0.32x = 1.32x \]

### Step 3: Set Up the Equation
According to the problem, the difference between the selling price at 32% profit and 18% profit is ₹112:
\[ SP_{32\%} - SP_{18\%} = 112 \]
Substituting the expressions we found:
\[ 1.32x - 1.18x = 112 \]

### Step 4: Simplify the Equation
\[ 0.14x = 112 \]

### Step 5: Solve for Cost Price (CP)
To find x, divide both sides by 0.14:
\[ x = \frac{112}{0.14} = 800 \]
So, the cost price (CP) of the article is ₹800.

### Step 6: Calculate Selling Price at 25% Profit
Now, we will find the selling price if the article were sold at 25% profit:
\[ SP_{25\%} = CP + 25\% \text{ of } CP = x + 0.25x = 1.25x \]
Substituting the value of x:
\[ SP_{25\%} = 1.25 \times 800 = 1000 \]

### Final Answer
The selling price of the article if it were sold at 25% profit is ₹1000.

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