Question

If tax on commodity is decreased by $15\%$ and its consumption increases by $10\%$, then the percentage decrease in the revenue is:

• A. $15\%$
• B. $8\frac{1}{2}\%$
• C. $6\frac{1}{2}\%$
• D. $5\%$

Answer 1

Answer: (C)

$6\frac{1}{2}\%$

Revenue is directly proportional to consumption $\left(C\right)$ and tax $\left(T\right)$.
Initial revenue $=C\times T$
when tax decrease by $15\%$ and consumption increases by $10\%$
New revenue $=(C+\frac{10}{100}C)\times (T-\frac{15}{100}T)$
New revenue $=\frac{110C}{100}\times \frac{85T}{100}$
New revenue $=0.935\times C\times T$
Thus, $\%$ decrease in revenue $=\frac{C\times T-0.935\times C\times T}{C\times T}\times 100=6.5\%$