How much per cent above the cost price should a shopkeeper mark his goods so that after allowing a discount of 25% on the marked price, he gain 20% ?

Options

A. 60%
B. 45%
C. 30%
D. 66%

Answer

To solve the problem, we need to determine how much percent above the cost price a shopkeeper should mark his goods to achieve a 20% profit after allowing a 25% discount on the marked price.

### Step-by-step Solution:

1. **Define Variables**:
- Let the Cost Price (CP) be \( x \).
- The shopkeeper wants to gain a profit of 20%, so the Selling Price (SP) will be:
\[ SP = CP + 20\% \text{ of } CP = x + 0.2x = 1.2x \]

2. **Calculate the Marked Price (MP)**:
- The shopkeeper allows a discount of 25% on the Marked Price (MP). Therefore, the Selling Price can also be expressed in terms of the Marked Price:
\[ SP = MP - 25\% \text{ of } MP = MP - 0.25 \times MP = 0.75 \times MP \]

3. **Set the Two Expressions for Selling Price Equal**:
- From the two expressions for SP, we have:
\[ 1.2x = 0.75 \times MP \]

4. **Solve for Marked Price (MP)**:
- Rearranging the equation gives:
\[ MP = \frac{1.2x}{0.75} = \frac{1.2}{0.75} \times x = 1.6x \]

5. **Calculate the Percentage Above Cost Price**:
- The difference between the Marked Price and Cost Price is:
\[ MP - CP = 1.6x - x = 0.6x \]
- To find the percentage above the Cost Price:
\[ \text{Percentage} = \left(\frac{MP - CP}{CP}\right) \times 100 = \left(\frac{0.6x}{x}\right) \times 100 = 60\% \]

### Final Answer:
The shopkeeper should mark his goods **60% above the cost price**.