Question:medium

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:

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Equal and opposite percentage changes never cancel; the net effect is a decrease of $\dfrac{x^2}{100}%$.
Updated On: Jul 15, 2026
  • 4% increase
  • 4% decrease
  • 5% increase
  • 5% decrease
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The Correct Option is B

Approach Solution - 1

Step 1: Set up sample values.
Assume the original price is Rs. 100 per unit and the original monthly consumption is 100 units, so the original bill is \( 100 \times 100 = 10000 \) rupees. Using round numbers like this makes the percentage change easy to read off directly.

Step 2: Apply the price rise.
The tax rises by 20%, so the new price per unit is \( 100 + 20\% \text{ of } 100 = 120 \) rupees.

Step 3: Apply the fall in consumption.
Consumption drops by 20%, so the new consumption is \( 100 - 20\% \text{ of } 100 = 80 \) units. The new bill is \( 120 \times 80 = 9600 \) rupees.

Step 4: Compare the bills.
The bill fell from 10000 to 9600 rupees, a drop of 400 rupees. As a percentage of the original bill, \( \frac{400}{10000} \times 100 = 4\% \).
\[ \boxed{4\% \text{ decrease}} \]
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Approach Solution -2

A quick way to handle successive percentage changes is to convert each change into a multiplying percentage and multiply those percentages together directly, then compare the result against each option.

  1. 4% increase: The tax rise means the new price is 120% of the old price, and the consumption fall means the new consumption is 80% of the old amount. Multiplying these percentages, \( 120\% \times 80\% = \frac{120}{100} \times \frac{80}{100} \times 100\% = 96\% \), which is below 100%, so an increase of any size is not possible here.
  2. 4% decrease: Since the combined effect works out to 96% of the original bill, the bill has fallen by \( 100\% - 96\% = 4\% \), matching this option precisely.
  3. 5% increase: Ruled out immediately since the combined percentage came out below 100%, not above it.
  4. 5% decrease: This would require the combined multiplier to work out to 95%, but the actual multiplication gives 96%, so this option is off by one percentage point and does not match.

Multiplying the two percentage changes directly shows the new bill settles at 96% of the original, a net fall of 4%.

So the correct answer is 4% decrease.

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