An article is sold at a profit of 20%. If it had been sold at a profit of 25%, it would have fetched 35 more. The cost price of the article is:

Options

A. 650
B. 700
C. 750
D. 800

Answer

To find the cost price of the article, we can follow these steps:

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

### Step 2: Calculate Selling Prices
1. Selling Price at 20% profit:
\[ SP_{20} = CP + 0.20 \times CP = 1.20 \times CP \]

2. Selling Price at 25% profit:
\[ SP_{25} = CP + 0.25 \times CP = 1.25 \times CP \]

### Step 3: Set Up the Equation
According to the problem, if the article were sold at a profit of 25%, it would have fetched 35 more than when sold at a profit of 20%. Therefore, we can write the equation:
\[ SP_{25} = SP_{20} + 35 \]

Substituting the expressions for \( SP_{20} \) and \( SP_{25} \):
\[ 1.25 \times CP = 1.20 \times CP + 35 \]

### Step 4: Simplify the Equation
Now, we can simplify the equation:
\[ 1.25 \times CP - 1.20 \times CP = 35 \]
\[ 0.05 \times CP = 35 \]

### Step 5: Solve for Cost Price
To find \( CP \), divide both sides by 0.05:
\[ CP = \frac{35}{0.05} = 700 \]

### Conclusion
The cost price of the article is \( \text{CP} = 700 \).

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