If the length of a rectangle is increased by 25% and its breadth is decreased by 20%, what happens to its area?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → It remains unchanged
Area \(=\) length \(\times\) breadth, so the new area is the old area times both change factors.
New length \(=1.25l\), new breadth \(=0.80b\)
New area \(=1.25\times0.80\times lb=1.00\times lb\)
The area stays the same
Why the other options are incorrect
Option (1) It increases by 5% — Incorrect. This simply takes \(25-20=5\); the changes must be multiplied as factors, \(1.25\times0.8=1\).
Option (2) It decreases by 5% — Incorrect. The product of the factors is exactly 1, so the area does not fall.
Option (4) It decreases by 1% — Incorrect. A 1% fall would come from \(\pm10\%\) changes; here \(1.25\times0.8=1\) exactly.