The price of an article is first increased by 20% and subsequently decreased by 25% due to reduction in sales. Find the net percentage change in price of the article.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 10% decrease
The 25% decrease is taken on the increased price, not on the original one, so the two changes cannot just be subtracted.
Assuming the original price to be 100:
After the 20% increase: \(100+20=120\)
25% of 120 \(=30\), so after the decrease: \(120-30=90\)
The price falls from 100 to 90: a net decrease of 10%
Shortcut: Multiply the two change factors.
Increase of 20%: factor 1.2; decrease of 25%: factor 0.75
\(1.2\times0.75=0.9\), that is, 90% of the original price, a 10% decrease