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).

Answer 2

The question asks for the overall change in the water bill when the tax rate rises by 20% but consumption falls by 20%. Instead of multiplying decimals, we can check this using simple fractions and then match against the given options.

1. 4% increase: A 20% rise in price scales the bill by a factor of \( \frac{6}{5} \), and a 20% fall in usage scales it by \( \frac{4}{5} \). Multiplying these fractions gives \( \frac{6}{5} \times \frac{4}{5} = \frac{24}{25} \), which is less than 1, so the bill cannot end up higher than before. This option does not match.
2. 4% decrease: Since \( \frac{24}{25} = 0.96 \), the new bill is 96% of the old one, which is exactly a 4% fall from the original amount. This matches the fraction worked out above.
3. 5% increase: This would require the combined factor to be \( \frac{21}{20} \), which does not match \( \frac{24}{25} \), so this option can be ruled out.
4. 5% decrease: This would need a factor of \( \frac{19}{20} = 0.95 \), which again does not equal \( \frac{24}{25} = 0.96 \), so this is not correct either.

Only the 4% decrease option lines up with the combined fraction \( \frac{24}{25} \) obtained from a 20% price rise and a 20% usage drop acting together.

So the correct answer is 4% decrease.

Answer 3

Rather than working through the general algebra, it helps to plug in a simple concrete example: say the original rate is Rs. 50 per unit and the original monthly consumption is 40 units, giving an original bill of Rs. 2000. Applying the 20% tax rise and 20% consumption fall to these specific numbers and comparing against each option settles the question.

1. 4% increase: With the new rate at Rs. 60 per unit (20% more than 50) and new consumption at 32 units (20% less than 40), the new bill is \( 60 \times 32 = 1920 \), which is lower than the original 2000, so an increase of any kind is ruled out.
2. 4% decrease: The new bill of Rs. 1920 is Rs. 80 less than the original Rs. 2000, and \( \frac{80}{2000} \times 100 = 4\% \), matching this option exactly.
3. 5% increase: Already ruled out since the bill fell rather than rose, so no increase figure applies here.
4. 5% decrease: A 5% fall on Rs. 2000 would mean a drop of Rs. 100, but the actual drop calculated is only Rs. 80, so this does not match.

Testing with concrete sample figures confirms the bill falls by exactly 4%, regardless of which specific price and consumption values are chosen to start with.

So the correct answer is 4% decrease.