Correct Answer – Option 4 : 4% decrease

Given:

Water tax is increased by 20% but its consumption is decreased by 20%.

Calculations:

Let the expenditure of water consumption be Rs. y and the tax imposed is x%.

so the tax needs to be paid = Rs. (x/100) × y = Rs. xy/100

Now new tax = (x × 120/100)% = (6x/5)%

and new expenditure = Rs. y × 80/100 = Rs. 4y/5

new tax = Rs. (6x/500) × 4y/5 = Rs. 24xy/2500

so change in tax = xy/100 – 24xy/2500 = xy/2500

then percentage change = (change/original) × 100

⇒ \(\frac{\frac{xy}{2500}}{\frac{xy}{100}}\ ×\ 100\ = \) (1/25) × 100 = 4% decrease (since new tax is less than original tax)

∴ The correct answer is 4%.

Short Tricks:

1.2 × 0.8 = 0.96 = 96 % (4 % decrease from original)