A man's income is increased by ₹ 1200 and at the same time, the rate of tax to be paid is reduced from 12\% to 10\%. He now pays the same amount of tax as before. What is his increased income if 20\% of his income is exempted from tax in both cases?
(a)₹ 4500
(b)₹ 6300
(c)₹ 6500
(d)₹ 7200
Answer
Answer (as printed): D
Explanation
Let the man's original income be ₹ $x$. Then, original tax paid $=₹[12 \%$ of ( $80 \%$ of $x$ )] $$=₹\left(\frac{12}{100} \times \frac{80}{100} \times x\right)=₹ \frac{12 x}{125} .$$ New income $=₹(x+1200)$. New tax paid $=₹[10 \%$ of $\{80 \%$ of $(x+1200)\}]$ $$\begin{aligned} & =₹\left[\frac{10}{100} \times \frac{80}{100} \times(x+1200)\right] \\ & =₹\left[\frac{2}{25}(x+1200)\right]=₹\left(\frac{2 x}{25}+96\right) . \end{aligned}$$ $\therefore \frac{12 x}{125}=\frac{2 x}{25}+96 \Rightarrow \frac{2 x}{125}=96 \Rightarrow x=\frac{96 \times 125}{2}=6000$. Hence, increased income $=₹(6000+1200)=₹ 7200$.
Explanation as extracted from the printed page; notation may be imperfect.