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If the price of a book is the first increased by 20% and then decreased by 20%. What is the net change in the price of the book?
- a)No change
- b)4% increase
- c)4% decrease
- d)10% decrease
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
If the price of a book is the first increased by 20% and then decrease...
Short Trick:
Net percentage change = 20 – 20 + 20 × (-20)/100 = -4%
∴ There is a decrease of 4%.
Net percentage change = 20 – 20 + 20 × (-20)/100 = -4%
∴ There is a decrease of 4%.
Detailed solution:
Let the original price of the book be Rs x.
∴ After increase of 20% in price
⇒ x + [x × (20/100)] = Rs 1.2x
∴ After decrease of 20% in price
⇒ 1.2x – [1.2x × (20/100)] = 0.96x
∴ Net decrease in the price of book
⇒ [(x – 0.96x)/x] × 100% = 4%
∴ Price of the book is decreased 4%.
Let the original price of the book be Rs x.
∴ After increase of 20% in price
⇒ x + [x × (20/100)] = Rs 1.2x
∴ After decrease of 20% in price
⇒ 1.2x – [1.2x × (20/100)] = 0.96x
∴ Net decrease in the price of book
⇒ [(x – 0.96x)/x] × 100% = 4%
∴ Price of the book is decreased 4%.
Most Upvoted Answer
If the price of a book is the first increased by 20% and then decrease...
Problem:
If the price of a book is first increased by 20% and then decreased by 20%, what is the net change in the price of the book?
Solution:
To find the net change in the price of the book, we need to calculate the final price after the two changes and compare it to the original price.
Step 1: Increase the price by 20%:
To increase the price of the book by 20%, we multiply the original price by 1 + 20% (or 0.2):
Increased price = Original price * (1 + 0.2)
Step 2: Decrease the price by 20%:
To decrease the price of the book by 20%, we multiply the increased price by 1 - 20% (or 0.2):
Final price = Increased price * (1 - 0.2)
Step 3: Calculate the net change:
To find the net change, we need to compare the final price to the original price:
Net change = (Final price - Original price) / Original price * 100%
Now let's calculate the net change in the price of the book.
Original price: Let's assume the original price of the book is $100.
Step 1: Increase the price by 20%:
Increased price = $100 * (1 + 0.2) = $120
Step 2: Decrease the price by 20%:
Final price = $120 * (1 - 0.2) = $96
Step 3: Calculate the net change:
Net change = ($96 - $100) / $100 * 100% = -$4 / $100 * 100% = -4%
The net change in the price of the book is a 4% decrease. Therefore, the correct answer is option C: 4% decrease.
If the price of a book is first increased by 20% and then decreased by 20%, what is the net change in the price of the book?
Solution:
To find the net change in the price of the book, we need to calculate the final price after the two changes and compare it to the original price.
Step 1: Increase the price by 20%:
To increase the price of the book by 20%, we multiply the original price by 1 + 20% (or 0.2):
Increased price = Original price * (1 + 0.2)
Step 2: Decrease the price by 20%:
To decrease the price of the book by 20%, we multiply the increased price by 1 - 20% (or 0.2):
Final price = Increased price * (1 - 0.2)
Step 3: Calculate the net change:
To find the net change, we need to compare the final price to the original price:
Net change = (Final price - Original price) / Original price * 100%
Now let's calculate the net change in the price of the book.
Original price: Let's assume the original price of the book is $100.
Step 1: Increase the price by 20%:
Increased price = $100 * (1 + 0.2) = $120
Step 2: Decrease the price by 20%:
Final price = $120 * (1 - 0.2) = $96
Step 3: Calculate the net change:
Net change = ($96 - $100) / $100 * 100% = -$4 / $100 * 100% = -4%
The net change in the price of the book is a 4% decrease. Therefore, the correct answer is option C: 4% decrease.
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If the price of a book is the first increased by 20% and then decreased by 20%. What is the net change in the price of the book?a)No changeb)4% increasec)4% decreased)10% decreaseCorrect answer is option 'C'. Can you explain this answer?
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