Question

The Municipality of a town increases water tax by 20% and water consumption decreased by 20%. Then the percentage of increase or decrease in the monthly expenditure is:

• A. 4% increase
• B. 4% decrease
• C. 5% increase
• D. 5% decrease

Hint:

Equal and opposite percentage changes never cancel; the net effect is a decrease of $\dfrac{x^2}{100}%$.

Answer 1

The Correct Option is B

Let the original price per unit be Rs.\ $p$ and consumption be $q$ units. Initial monthly expenditure $=pq$.
New price $=1.20p$ (20% higher). New consumption $=0.80q$ (20% lower).
New expenditure $=(1.20p)\times(0.80q)=0.96\,pq$, which is $96%$ of the old bill.
Hence the expenditure falls by $100%-96%=4%$.
Shortcut: for successive percentage changes use $a+b+\dfrac{ab}{100}$. With $a=+20,\ b=-20$:
$20-20+\dfrac{(20)(-20)}{100} = -4%$ (a 4% decrease).