Question 134

If tax on a commodity is reduced by 10%, total revenue remains unchanged. What is the percentage increase in its consumption?

Solution

Revenue = consumption $$\times$$ tax amount

Let consumption = 10 and tax = 10

=> Revenue = $$10 \times 10 = 100$$

Now, after tax is reduced by 10 %, new tax = $$10 - \frac{10}{100} \times 10$$

= $$10 - 1 = 9$$

Total revenue remains unchanged

=> New consumption = $$\frac{100}{9}$$

$$\therefore$$ % increase in consumption = $$\frac{\frac{100}{9} - 10}{10} \times 100$$

= $$\frac{10}{9} \times 10 = \frac{100}{9}$$

= $$11\frac{1}{9} \%$$

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