A merchant makes a profit of 20% by selling an article. What would be the percentage change in the profit percent had he paid 10% less for it and the customer paid 10% more for it?

Answer

To solve the problem, we will follow these steps:

### Step 1: Define the Cost Price (CP) and Selling Price (SP)
Let the cost price (CP) of the article be \( x \).

Since the merchant makes a profit of 20%, the selling price (SP) can be calculated as:
\[ SP = CP + Profit = x + 0.20x = 1.20x \]

### Step 2: Calculate the New Cost Price
If the merchant pays 10% less for the article, the new cost price (CP') will be:
\[ CP' = CP - 10\% \text{ of } CP = x - 0.10x = 0.90x \]

### Step 3: Calculate the New Selling Price
If the customer pays 10% more for the article, the new selling price (SP') will be:
\[ SP' = SP + 10\% \text{ of } SP = 1.20x + 0.10 \times 1.20x = 1.20x + 0.12x = 1.32x \]

### Step 4: Calculate the New Profit
Now, we can calculate the new profit using the new CP' and SP':
\[ \text{New Profit} = SP' - CP' = 1.32x - 0.90x = 0.42x \]

### Step 5: Calculate the New Profit Percentage
The new profit percentage (Profit%) can be calculated as:
\[ \text{Profit%} = \left( \frac{\text{New Profit}}{CP'} \right) \times 100 = \left( \frac{0.42x}{0.90x} \right) \times 100 = \frac{0.42}{0.90} \times 100 \approx 46.67\% \]

### Step 6: Calculate the Change in Profit Percentage
Now, we can find the change in profit percentage:
\[ \text{Change in Profit%} = \text{New Profit%} - \text{Original Profit%} = 46.67\% - 20\% = 26.67\% \]

### Step 7: Calculate the Percentage Change in Profit Percentage
Finally, we can calculate the percentage change in profit percentage:
\[ \text{Percentage Change} = \left( \frac{\text{Change in Profit%}}{\text{Original Profit%}} \right) \times 100 = \left( \frac{26.67}{20} \right) \times 100 \approx 133.35\% \]

### Final Answer:
The percentage change in the profit percentage is approximately **133.35%**.

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