The length of a rectangle is increased by 20% and its breadth is increased by 10%. What is the percentage increase in its area?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 32%
Area \(=\) length \(\times\) breadth, so the two percentage changes multiply; they are not simply added.
New length \(=1.2\,l\), new breadth \(=1.1\,b\)
New area \(=1.2\times1.1\times lb=1.32\,lb\)
Increase \(=1.32-1=0.32\), that is 32%
The area increases by 32%.
Why the other options are incorrect
Option (1) 30% — Incorrect. This just adds 20% and 10% and leaves out the extra \(20\%\) of \(10\%=2\%\).
Option (2) 28% — Incorrect. This takes away the 2% instead of adding it.
Option (4) 50% — Incorrect. The new area is \(1.2\times1.1=1.32\) times the old one, not 1.5 times, so the rise is 32%.