The price of an article is reduced by 10%. To restore its original price, how much percentage increase must be done in new price ?

Question

Accepted Answer

To solve the problem of determining the percentage increase required to restore the original price after a 10% reduction, let's break down the process step by step.

### Explanation for Option 4:

1. **Initial Price and Reduction:**
   - Let's assume the original price of the article is $100.
   - A 10% reduction in price means the price is reduced by $10 (10% of $100).
   - Therefore, the new price after reduction is $100 - $10 = $90.

2. **Restoring the Original Price:**
   - To restore the original price of $100 from the reduced price of $90, we need to calculate the percentage increase required.
   - The increase needed is $100 - $90 = $10.

3. **Calculating the Percentage Increase:**
   - The percentage increase is calculated based on the reduced price ($90).
   - Percentage increase = (Increase / Reduced Price) × 100
   - Percentage increase = ($10 / $90) × 100 = 11.11%

4. **Converting to Fraction:**
   - The percentage 11.11% can be expressed as a fraction: $11\frac{1}{9}$%.
   - Therefore, the correct option is 4: $11\frac{1}{9}$%.

### Explanation for Why Other Options are Incorrect:

1. **Option 1 (10%):**
   - A 10% increase on the reduced price of $90 would result in an increase of $9 (10% of $90).
   - This would make the new price $90 + $9 = $99, which is still $1 short of the original price of $100.

2. **Option 2 ($9\frac{1}{11}$%):**
   - A $9\frac{1}{11}$% increase on $90 would result in an increase of approximately $8.18.
   - This would make the new price $90 + $8.18 = $98.18, which is less than the original price of $100.

3. **Option 3 (11%):**
   - An 11% increase on $90 would result in an increase of $9.90 (11% of $90).
   - This would make the new price $90 + $9.90 = $99.90, which is still slightly less than the original price of $100.

In conclusion, the only option that correctly restores the original price of $100 from the reduced price of $90 is Option 4: $11\frac{1}{9}$%.