The price of an article was decreased by 10% and again reduced by 10%. By what percent should the price have been reduced once, In order to produce the same effect as these two successive reductions?

Options

A. 0.15
B. 0.1
C. 0.2
D. 0.25

Answer

To solve the problem of determining the single percentage reduction that would have the same effect as two successive 10% reductions, we can follow these steps:

### Step-by-Step Solution:

1. **Initial Price Representation**:
Let the initial price of the article be represented as \( P \).

2. **First Reduction**:
The first reduction is 10%. Therefore, the price after the first reduction can be calculated as:
\[ \text{Price after first reduction} = P - 0.10P = 0.90P \]

3. **Second Reduction**:
The second reduction is also 10%, but this time it is applied to the new price \( 0.90P \). The price after the second reduction can be calculated as:
\[ \text{Price after second reduction} = 0.90P - 0.10(0.90P) = 0.90P \times 0.90 = 0.81P \]

4. **Total Reduction Calculation**:
Now, we need to find the total reduction from the original price \( P \) to the final price \( 0.81P \). The reduction in price is:
\[ \text{Reduction} = P - 0.81P = 0.19P \]

5. **Percentage Reduction**:
To find the percentage reduction, we calculate:
\[ \text{Percentage Reduction} = \left( \frac{\text{Reduction}}{\text{Original Price}} \right) \times 100 = \left( \frac{0.19P}{P} \right) \times 100 = 19\% \]

### Final Answer:
The price should have been reduced by **19%** to produce the same effect as the two successive reductions of 10%.