An article is sold at 25% profit. If its CP and SP are more by Rs 20 and Rs 4 respectively, the percentage of profit decreases by 15%. Find the cost price.

Answer

To solve the problem, we need to find the cost price (CP) of an article given that it is sold at a 25% profit, and that if the CP and selling price (SP) are increased by Rs 20 and Rs 4 respectively, the percentage of profit decreases by 15%.

Let's denote:
- CP = Cost Price
- SP = Selling Price

### Step 1: Establish the initial profit relationship
Since the article is sold at a 25% profit, we can express the selling price in terms of the cost price:
\[ SP = CP + 0.25 \times CP = 1.25 \times CP \]

### Step 2: Set up the new conditions
According to the problem, if the CP increases by Rs 20 and the SP increases by Rs 4, the new CP and SP can be expressed as:
- New CP = CP + 20
- New SP = SP + 4

### Step 3: Calculate the new selling price
Using the expression for SP from Step 1:
\[ New SP = 1.25 \times CP + 4 \]

### Step 4: Calculate the new profit percentage
The new profit can be calculated as:
\[ New Profit = New SP - New CP \]
Substituting the values:
\[ New Profit = (1.25 \times CP + 4) - (CP + 20) \]
\[ New Profit = 1.25CP + 4 - CP - 20 \]
\[ New Profit = 0.25CP - 16 \]

### Step 5: Establish the new profit percentage
The new profit percentage is given to be 10% (25% - 15%):
\[ \frac{New Profit}{New CP} \times 100 = 10 \]
Substituting the values:
\[ \frac{0.25CP - 16}{CP + 20} \times 100 = 10 \]

### Step 6: Solve the equation
To simplify, we can multiply both sides by (CP + 20):
\[ 0.25CP - 16 = 0.10 \times (CP + 20) \]
Expanding the right side:
\[ 0.25CP - 16 = 0.10CP + 2 \]

Now, rearranging the equation:
\[ 0.25CP - 0.10CP = 2 + 16 \]
\[ 0.15CP = 18 \]
\[ CP = \frac{18}{0.15} \]
\[ CP = 120 \]

### Final Answer
The cost price of the article is Rs 120.

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