A shopkeeper buys an article on discount of 20% on MP. Shopkeeper marks it Rs 200 more than CP and gives 10% discount on it. Profit gained is Rs 148. Find initial M.P.

Answer

To solve the problem step by step, we will use the information given in the question and apply the formulas related to profit, loss, and discounts.

### Step 1: Define Variables
Let the initial Mark Price (MP) be \( x \).

### Step 2: Calculate Cost Price (CP)
Since the shopkeeper buys the article at a discount of 20% on MP, the Cost Price (CP) can be calculated as:
\[ CP = MP - (20\% \text{ of } MP) = x - 0.2x = 0.8x \]

### Step 3: Determine Marked Price (MP) in relation to CP
According to the problem, the shopkeeper marks the article Rs 200 more than the CP:
\[ MP = CP + 200 \]
Substituting the value of CP from Step 2:
\[ x = 0.8x + 200 \]

### Step 4: Solve for x
Rearranging the equation:
\[ x - 0.8x = 200 \]
\[ 0.2x = 200 \]
\[ x = \frac{200}{0.2} = 1000 \]

### Step 5: Calculate Selling Price (SP)
The shopkeeper gives a 10% discount on the marked price:
\[ SP = MP - (10\% \text{ of } MP) = x - 0.1x = 0.9x \]
Substituting the value of \( x \):
\[ SP = 0.9 \times 1000 = 900 \]

### Step 6: Calculate Profit
The profit gained is given as Rs 148. The profit can also be expressed as:
\[ Profit = SP - CP \]
Substituting the values of SP and CP:
\[ 148 = 900 - 0.8 \times 1000 \]
Calculating CP:
\[ CP = 0.8 \times 1000 = 800 \]
Now substituting CP into the profit equation:
\[ 148 = 900 - 800 \]
This confirms that the calculations are correct.

### Final Answer
Thus, the initial Mark Price (MP) is:
\[ \text{MP} = 1000 \]