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If the tax on an article is reduced by 20% and its consumption increases by 15%, what will be the effect on the tax revenue?
It increases by 10%
It decreases by 8%
It increases by 8%
No change
It decreases by 8%
Use successive percentage change formula (net effect = a + b + ab/100). Here, a = -20 and b = 15.
Tax is reduced by 20% and consumption is increased by 15%.
Net┬аPercentage┬аChange=x+y+100x├ЧyтАЛ
Use successive percentage change formula (net effect = a + b + ab/100). Here, a = -20 and b = 15.
Do not simply subtract 20% from 15%. The net revenue is a product of tax rate and consumption.
Step 1: Identify the given percentage changes
Let the tax rate decrease by a=тИТ20% and the consumption increase by b=+15%.
a=тИТ20,b=+15
Step 2: Apply the successive percentage formula
Tax revenue is the product of tax rate and consumption. The net percentage change formula is given by a+b+100a├ЧbтАЛ.
Net┬аEffect=тИТ20+15+100(тИТ20)├Ч15тАЛ
Step 3: Simplify and calculate the final value
Substitute the values: тИТ20+15=тИТ5, and 100тИТ300тАЛ=тИТ3. Adding them gives тИТ5тИТ3=тИТ8%.
Net┬аEffect=тИТ5тИТ3=тИТ8%
Step 4: Conclusion
A negative sign indicates a decrease. Therefore, the tax revenue decreases by 8%.
8%┬аdecrease
B is correct because the successive percentage formula yields a net decrease of 8% in tax revenue.
This successive formula is widely applicable in profit & loss, geometry (area/volume changes), and economics problems involving product of two variables.