The ratio of cost price and selling price of an article is 20 : 21. What is the gain per cent on it ?

Options

A. 0.05
B. `5 1/2%`
C. 0.06
D. `6 1/4%`

Answer

To solve the problem step by step, we will follow the given information about the ratio of cost price (CP) and selling price (SP) and calculate the gain percentage.

### Step 1: Understand the ratio
The ratio of cost price to selling price is given as 20:21. This means:
- Cost Price (CP) = 20 parts
- Selling Price (SP) = 21 parts

### Step 2: Assign values to CP and SP
To make calculations easier, we can assign a value to each part. Let's assume:
- CP = 20 rupees
- SP = 21 rupees

### Step 3: Calculate the gain
Gain can be calculated using the formula:
\[ \text{Gain} = \text{Selling Price} - \text{Cost Price} \]
Substituting the values:
\[ \text{Gain} = SP - CP = 21 - 20 = 1 \text{ rupee} \]

### Step 4: Calculate the gain percentage
The gain percentage can be calculated using the formula:
\[ \text{Gain Percentage} = \left( \frac{\text{Gain}}{\text{Cost Price}} \right) \times 100 \]
Substituting the values:
\[ \text{Gain Percentage} = \left( \frac{1}{20} \right) \times 100 \]

### Step 5: Solve for gain percentage
Calculating the above expression:
\[ \text{Gain Percentage} = \left( \frac{1}{20} \right) \times 100 = 5\% \]

### Final Answer
The gain percentage on the article is **5%**.

---