Question

A man's income is increased by Rs 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 the cases ?

• A. Rs 6300
• B. Rs 7200
• C. Rs 4500
• D. Rs 6500

Answer 1

Answer: (B)

Rs 7200

Let the man's original income = x in Rs.

Then the taxable income = $x-x\times \frac{20}{100}=\frac{4x}{5}$.

$\therefore$ The tax at 12%=$\frac{4x}{5}\times \frac{12}{100}=\frac{12x}{125.}$$\frac{4x}{5}\times \frac{12}{100}=\frac{12x}{125.}$.

After an increament of Rs1200 his new income=x+1200 in Rs.

Then the taxable income=$(x+1200)-(x+1200)\times \frac{20}{100}=\frac{4x+4800}{5}$.

$\therefore$ The tax at 10%= $\frac{4x+4800}{5}\times \frac{10}{100}=\frac{2x+2400}{25}$

So, by the given condition,

$\frac{2x+2400}{25}=\frac{12x}{125.}$.

Or 10x + 12000 = 12x

Or 2x = 12000

Or x = 6000.

$\therefore$ His increased income = x + 1200 = Rs ( 6000 + 1200 )

= Rs 7200 (Option B)