Question

Calculate percentage increase after 25% discount and 30% increase on $120

Answer 1

To find the percentage increase after applying a 25% discount followed by a 30% increase on an initial amount of $120, let's break it down step by step.

1. **Calculate the amount after the 25% discount**:
- A 25% discount on $120 is calculated as:
\[
\text{Discount} = 120 \times 0.25 = 30
\]
- Subtract the discount from the original price:
\[
\text{Price after discount} = 120 - 30 = 90
\]

2. **Calculate the amount after the 30% increase**:
- A 30% increase on $90 is calculated as:
\[
\text{Increase} = 90 \times 0.30 = 27
\]
- Add the increase to the discounted price:
\[
\text{Price after increase} = 90 + 27 = 117
\]

3. **Calculate the overall percentage change from the original price**:
- The original price was $120, and the final price after discount and increase is $117.
- The overall change in amount is:
\[
\text{Change} = 117 - 120 = -3
\]
- To find the percentage change:
\[
\text{Percentage change} = \left(\frac{\text{Change}}{\text{Original Price}}\right) \times 100 = \left(\frac{-3}{120}\right) \times 100 = -2.5\%
\]

So the final result is that there is a **2.5% decrease** from the original price after the discount and subsequent increase.