Q109
ArithmeticGeometry & Mensuration
The length of a rectangle is decreased by 20% while the breadth is increased by 20%. Then the area of the rectangle will
- a.remain unchanged.
- b.decrease by 4%.
- c.increase by 2%.
- d.increase by 4%.
Answer: (B) decrease by 4%.
New area $= (0.8L) \times (1.2B) = 0.96\,LB$, i.e. 96% of the original, a decrease of 4%. General rule: when one dimension increases by $x\%$ and the other decreases by $x\%$, the area always falls by $\frac{x^2}{100}\%$; here $\frac{20^2}{100} = 4\%$. For unequal changes of $a\%$ and $b\%$ the net change is $a + b + \frac{ab}{100}$, which gives $20 - 20 - \frac{400}{100} = -4\%$. Option A is the usual trap of assuming that equal percentage increase and decrease cancel out. The same $\frac{x^2}{100}$ rule gives the net loss when two articles are sold at one price with equal profit and loss percentages.