Consider the following statements:
I. If a price is first increased by 20% and then decreased by 20%, the final price is 4% less than the original price.
II. Two successive increases of 10% each are equal to a single increase of 20%.
Which of the above statements is/are correct?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Only I
Successive percentage changes multiply: each change is taken on the value left by the previous one, so the changes cannot simply be added.
I. If a price is first increased by 20% and then decreased by 20%, the final price is 4% less than the original price. — Correct. The two changes multiply, so the final price is \(1.20\times0.80=0.96\) times the original.
Take the original price as 100
After the 20% increase: \(100\times1.20=120\)
After the 20% decrease: \(120\times0.80=96\)
Fall \(=100-96=4\), that is 4% less
II. Two successive increases of 10% each are equal to a single increase of 20%. — Incorrect. The second 10% is taken on the increased value, so the single equivalent increase is 21%, not 20%.
Take the original value as 100
After the first 10% increase: \(110\)
After the second 10% increase: \(110\times1.10=121\)
Single equivalent increase \(=121-100=21\%\)