A shopkeeper allows a discount of 4% on his article. If cost price of the article is X 100 and he wants to get a profit of 20%. Then, its marked price will be

Options

A. X 96
B. X 120
C. X 125
D. X 130

Answer

To find the marked price of the article given a cost price of 100 and a desired profit of 20% with a discount of 4%, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Cost Price (CP):**
- The cost price of the article is given as \( CP = 100 \).

2. **Calculate the Selling Price (SP) for a 20% Profit:**
- To find the selling price that gives a 20% profit, we use the formula:
\[ SP = CP + (20\% \text{ of } CP) \]
- Calculate 20% of CP:
\[ 20\% \text{ of } 100 = \frac{20}{100} \times 100 = 20 \]
- Now, add this to the cost price:
\[ SP = 100 + 20 = 120 \]

3. **Determine the Discount:**
- The shopkeeper allows a discount of 4% on the marked price (MP).
- The selling price after the discount can be expressed as:
\[ SP = MP - (4\% \text{ of } MP) \]
- This can be rewritten as:
\[ SP = MP \times \left(1 - \frac{4}{100}\right) = MP \times 0.96 \]

4. **Set Up the Equation:**
- Since we know the selling price (SP) is 120, we can set up the equation:
\[ 120 = MP \times 0.96 \]

5. **Solve for the Marked Price (MP):**
- Rearranging the equation to find MP:
\[ MP = \frac{120}{0.96} \]
- Calculate MP:
\[ MP = 125 \]

### Final Answer:
The marked price of the article is \( \text{MP} = 125 \).

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