After giving 20% discount on an article there is a profit of 20%. What will be profit per cent when no discount is given ?

Options

A. 40
B. 44
C. 54
D. 50

Answer

To solve the problem, we need to determine the profit percentage when no discount is given, given that a 20% discount results in a 20% profit.

### Step-by-Step Solution:

1. **Understand the Terms**:
- Let the Cost Price (CP) of the article be \( CP \).
- Let the Marked Price (MP) be the price before any discount is applied.

2. **Calculate the Selling Price (SP) after Discount**:
- A 20% discount on the Marked Price means the Selling Price (SP) can be calculated as:
\[ SP = MP - (20\% \text{ of } MP) = MP \times (1 - 0.20) = MP \times 0.80 \]

3. **Determine the Selling Price with Profit**:
- Given that there is a 20% profit when selling at this SP, we can express this as:
\[ SP = CP + (20\% \text{ of } CP) = CP \times (1 + 0.20) = CP \times 1.20 \]

4. **Equate the Two Expressions for SP**:
- From the previous steps, we have:
\[ MP \times 0.80 = CP \times 1.20 \]

5. **Express MP in terms of CP**:
- Rearranging the equation gives us:
\[ MP = \frac{CP \times 1.20}{0.80} = CP \times \frac{1.20}{0.80} = CP \times 1.5 \]

6. **Calculate the Selling Price without Discount**:
- If no discount is given, the Selling Price is equal to the Marked Price:
\[ SP_{no\ discount} = MP = CP \times 1.5 \]

7. **Calculate the Profit when no Discount is Given**:
- The profit when no discount is given can be calculated as:
\[ \text{Profit} = SP_{no\ discount} - CP = (CP \times 1.5) - CP = CP \times 0.5 \]

8. **Calculate the Profit Percentage**:
- The profit percentage is given by:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{CP}\right) \times 100 = \left(\frac{CP \times 0.5}{CP}\right) \times 100 = 50\% \]

### Final Answer:
The profit percentage when no discount is given is **50%**.