(A) If a product's price is decreased by 25 % and then increased by 20%, then the net change in the price of the product, is: decrease by 10%
(B) If a product's price is increased by 15 % and then again increased by 20 %, then the net change in the price of the product, is: Increase by 38%
Choose the correct option(s):
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Both (A) and (B)
Successive percentage changes are applied one after another, each on the new price, so the price is multiplied by one factor for each change. A rise of 20% multiplies by 1.20; a fall of 25% multiplies by 0.75.
(A) If a product's price is decreased by 25 % and then increased by 20%, then the net change in the price of the product, is: decrease by 10% Correct. \(0.75\times1.20=0.90\), so the price ends at 90% of the original: a decrease of 10%.
(B) If a product's price is increased by 15 % and then again increased by 20 %, then the net change in the price of the product, is: Increase by 38% Correct. \(1.15\times1.20=1.38\), so the price ends at 138% of the original: an increase of 38%.
Tip: Two successive changes of \(a\%\) and \(b\%\) give a net change of \(\left(a+b+\frac{ab}{100}\right)\%\), with a fall taken as negative: \(-25+20-5=-10\) and \(15+20+3=38\).