A merchant sells an article by increasing its cost by 10% first, and then reducing it by 10%. What is the net effect to the merchant in that business?

Options

A. No loss- no profit
B. `1%` loss
C. `1%` profit
D. `2%` profit

Explanation

To solve the problem step by step, we will analyze the merchant's pricing strategy:

### Step 1: Define the initial cost
Let the initial cost of the article be \( C = 100 \) (this is a convenient choice to simplify calculations).

### Step 2: Calculate the increased price after a 10% increase
The merchant increases the cost by 10%. Therefore, the new price after the increase is calculated as follows:
\[ \text{Increased Price} = C + (10\% \text{ of } C) = 100 + (0.10 \times 100) = 100 + 10 = 110 \]

### Step 3: Calculate the price after a 10% reduction on the increased price
Now, the merchant reduces the new price by 10%. The reduction is calculated on the increased price of 110:
\[ \text{Reduction} = 10\% \text{ of } 110 = 0.10 \times 110 = 11 \]
Thus, the final selling price after the reduction is:
\[ \text{Final Selling Price} = 110 - 11 = 99 \]

### Step 4: Determine the net effect on the merchant
To find the net effect, we compare the final selling price with the original cost:
\[ \text{Net Effect} = \text{Final Selling Price} - \text{Original Cost} = 99 - 100 = -1 \]

This indicates that the merchant incurs a loss of 1.

### Step 5: Calculate the percentage loss
To express this loss as a percentage of the original cost:
\[ \text{Percentage Loss} = \left( \frac{\text{Loss}}{\text{Original Cost}} \right) \times 100 = \left( \frac{1}{100} \right) \times 100 = 1\% \]

### Conclusion
The net effect on the merchant is a loss of 1%.