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

Answer 1

The Correct Option is B

The correct option is (B): 4% decrease.

Answer 2

The question asks how the monthly water expenditure changes when the tax rate rises by 20% and consumption falls by 20%. Expenditure is the product of the rate and the quantity used, so we can test each option by checking whether it matches the actual product of the two percentage changes.

1. 4% increase: If tax and consumption changes fully cancelled out, expenditure would stay flat, and a 4% increase would only happen if both factors pushed spending up together. Since consumption fell rather than rose, this does not match the actual multiplier of \( 1.2 \times 0.8 = 0.96 \), which is below 1, not above it.
2. 4% decrease: Multiplying the new tax factor \( 1.2 \) (a 20% rise) by the new consumption factor \( 0.8 \) (a 20% fall) gives \( 1.2 \times 0.8 = 0.96 \), which is 4% less than the original factor of \( 1 \). This matches a net 4% decrease in expenditure exactly.
3. 5% increase: A 5% increase would require the product of the two factors to exceed \( 1 \) by 0.05, but \( 0.96 \) is below \( 1 \), so this does not fit.
4. 5% decrease: A 5% decrease would need the product to equal \( 0.95 \), but the actual product from a 20% rise and a 20% fall is \( 0.96 \), so this is off by one percentage point.

Testing the combined percentage change directly shows the expenditure factor lands at \( 0.96 \), a fall of exactly 4%, ruling out every other option.

Therefore, the correct answer is 4% decrease.

Answer 3

The question asks how a town's monthly water expenditure changes when the tax rate goes up by 20% while consumption falls by 20%. Since expenditure is simply rate multiplied by quantity used, picking convenient sample numbers and working out the actual new expenditure directly settles which option is correct.

1. 4% increase: Suppose the original rate is Rs. 10 per unit and original consumption is 100 units, giving an original expenditure of Rs. 1000. The new rate is \( 10 \times 1.2 = 12 \), and the new consumption is \( 100 \times 0.8 = 80 \), giving new expenditure \( 12 \times 80 = 960 \). Since 960 is less than 1000, expenditure has not increased at all, so this option is ruled out.
2. 4% decrease: From the same sample figures, new expenditure works out to Rs. 960 against an original of Rs. 1000, a fall of Rs. 40 out of 1000, which is exactly 4%.
3. 5% increase: Since the actual new expenditure of Rs. 960 is lower than the original Rs. 1000, there is no increase of any size, ruling this out as well.
4. 5% decrease: A 5% decrease would mean expenditure falling to Rs. 950, but the direct calculation gives Rs. 960, a full Rs. 10 higher than that, so this does not match either.

Working out the new expenditure directly from sample figures shows a fall to 96% of the original amount, a decrease of exactly 4%.

Therefore, the correct answer is 4% decrease.