If the ratio of the cost price and selling price of an article is 20 : 21, then what will be the profit percentage?

Options

A. a)`5%`
B. b)`4.5%`
C. c)`6%`
D. d)`7.5%`

Answer

To find the profit percentage when the ratio of the cost price (CP) to the selling price (SP) is given as 20:21, we can follow these steps:

### Step 1: Assign Variables
Let the cost price (CP) be represented as 20x and the selling price (SP) be represented as 21x, where x is a common multiplier.

### Step 2: Calculate Profit
Profit can be calculated using the formula:
\[ \text{Profit} = \text{Selling Price} - \text{Cost Price} \]
Substituting the values we have:
\[ \text{Profit} = SP - CP = 21x - 20x = 1x \]
So, the profit is \( x \).

### Step 3: Calculate Profit Percentage
Profit percentage is calculated using the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 \]
Substituting the values:
\[ \text{Profit Percentage} = \left( \frac{x}{20x} \right) \times 100 \]
This simplifies to:
\[ \text{Profit Percentage} = \left( \frac{1}{20} \right) \times 100 = 5\% \]

### Conclusion
The profit percentage is **5%**.

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