Income tax is raised from 4 paise to 5 paise in a rupee but the revenue is increa-sed by 10\% only. Find the decrease percent in the amount taxed.
(a)12
(b)14
(c)16
(d)None of these
Answer
Answer (as printed): A
Explanation
Let the original taxed amount be ₹ $x$ and new taxed amount be ₹ $y$. Let original revenue be ₹ 100. Then, 4\% of $x=100$ or $x=\left(\frac{100 \times 100}{4}\right)=₹ 2500$. New revenue $=110 \%$ of $₹ 100=₹ 110$. Then, 5\% of $y=110$ or $y=\left(\frac{110 \times 100}{5}\right)=₹ 2200$. Decrease in taxed amount $=₹(2500-2200)=₹ 300$. $$\text { ∴ Decrease } \%=\left(\frac{300}{2500} \times 100\right) \%=12 \% \text {. }$$
Explanation as extracted from the printed page; notation may be imperfect.