A number is first increased by 10% and then decreased by 10%. Then the net percentage increase or decrease in the number is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 1% decrease
The 10% decrease is taken on the increased number, which is bigger than the original, so the decrease is larger than the increase and the two do not cancel.
Assuming the number to be 100:
After the 10% increase: \(100+10=110\)
After the 10% decrease: \(110-11=99\)
Net change: 100 becomes 99, a decrease of 1%
Tip: For two successive changes of \(a\%\) and \(b\%\), the net change is \(\left(a+b+\frac{ab}{100}\right)\%\), with a decrease taken as negative. Here \(10-10-\frac{100}{100}=-1\), a 1% decrease; an equal rise and fall always ends in a small net loss.