If the price of a book is increased by 20% and then decreased by 20%, what is the net change in the price?
Practice Questions
1 question
Q1
If the price of a book is increased by 20% and then decreased by 20%, what is the net change in the price?
0%
4%
5%
6%
Let the original price be $100. After a 20% increase, the price becomes $120. After a 20% decrease, the price becomes $120 - 0.20 × 120 = $96. The net change is (96 - 100)/100 × 100 = -4%.
Questions & Step-by-step Solutions
1 item
Q
Q: If the price of a book is increased by 20% and then decreased by 20%, what is the net change in the price?
Solution: Let the original price be $100. After a 20% increase, the price becomes $120. After a 20% decrease, the price becomes $120 - 0.20 × 120 = $96. The net change is (96 - 100)/100 × 100 = -4%.
Steps: 7
Step 1: Assume the original price of the book is $100.
Step 2: Calculate the price after a 20% increase. 20% of $100 is $20, so the new price is $100 + $20 = $120.
Step 3: Calculate the price after a 20% decrease from the new price of $120. 20% of $120 is $24, so the new price is $120 - $24 = $96.
Step 4: Find the net change in price. The original price was $100 and the final price is $96.
Step 5: Calculate the change: $96 - $100 = -$4.
Step 6: To find the percentage change, divide the change by the original price: -$4 / $100 = -0.04.
Step 7: Convert to percentage by multiplying by 100: -0.04 × 100 = -4%.
