If the length of a rectangle is increased by 20% and its breadth is decreased by 15%, what happens to its area?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → It increases by 2%
Area = length × breadth, so the new area is the old area multiplied by both change factors.
New length \(=1.20\times\) old length
New breadth \(=0.85\times\) old breadth
New area \(=1.20\times0.85=1.02\times\) old area
The area increases by \((1.02-1)\times100=2\%\)
Why the other options are incorrect
Option (2) It decreases by 2% — Incorrect. The factor 1.02 is more than 1, so the area grows.
Option (3) It increases by 4% — Incorrect. A 4% rise needs a factor of 1.04, but \(1.20\times0.85=1.02\), so the gain is only 2%.
Option (4) It remains unchanged — Incorrect. A 20% rise and a 15% fall do not cancel; the product of the factors is 1.02, not 1.