Question

If tax on a 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 = consumption × tax amount per commodity
Let us assume,

Consumption(C) $=x$, Tax amount per commodity(T) $=y$
$⟹$ Revenue(R) $=xy$

$\therefore$ New consumption $=x+10\%ofx$

$=x+\frac{x\times 10}{100}$

$=\frac{110x}{100}$

$=\frac{11x}{10}$

And new tax amount per commodity $=y-15\%ofy$

$=y-\frac{y\times 15}{100}$

$=\frac{85y}{100}$

$=\frac{17y}{20}$
$\therefore$ New revenue $=\frac{11x}{10}\times \frac{17y}{20}$

$=\frac{187xy}{200}$
$\therefore$ Decrease in revenue $=xy-\frac{187xy}{200}$

$=\frac{13xy}{200}$

Percentage decrease in revenue $=\frac{\frac{13xy}{200}}{xy}\times 100$

$=\frac{13}{2}$

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

Hence, the decrease in revenue is $=6\frac{1}{2}\%$.