The price of a mobile phone is first increased by 20% and then decreased by…
2022
The price of a mobile phone is first increased by 20% and then decreased by 25%. What is the net percentage change in its final price?
Answer: A. 10% — ConceptFor successive percentage changes, multiply the corresponding price factors; percentages are not added or subtracted directly because the second change…
- A.
10%
- B.
18%
- C.
20%
- D.
12%
Attempted by 4 students.
Show answer & explanation
Correct answer: A
Concept
For successive percentage changes, multiply the corresponding price factors; percentages are not added or subtracted directly because the second change uses the already changed price as its base.
An increase of r% uses the factor (1 + r/100), while a decrease of s% uses the factor (1 - s/100). Compare the final factor with 1 to obtain the net change.
Application
Let the original mobile price be 100 units.
After the 20% increase, the price is 100 × 1.20 = 120 units.
After the 25% decrease, the price is 120 × 0.75 = 90 units.
Cross-check
The combined factor is 1.20 × 0.75 = 0.90. Since 0.90 is 0.10 below 1, the final price is 10% lower than the original price.
Therefore, the net percentage change is a 10% decrease.