When income tax is 3 paise in a rupee, a person's net income is ₹ 237650. What will it be when the income tax is raised to 7 paise?

Concept & Formula Net income is what remains after deducting income tax from gross income. $$ \text{Gross Income} = \frac{\text{Net Income}}{1 - \text{Tax Rate}} $$ Step-by-Step Solution * Given: Initial tax rate = $3\%$, Initial Net Income = ₹ $237650$. * If tax is $3$ paise in a rupee ($3\%$), net income is $97\%$ of gross income. * Gross Income = $\frac{237650}{0.97} = 245000$. * New tax rate = $7$ paise in a rupee ($7\%$). * New Net Income = $93\%$ of $245000$. * Calculation: $0.93 \times 245000 = 227850$. Exam Strategy & Shortcut Since the base (Gross Income) is the same, use direct proportionality: $\frac{\text{New Net}}{\text{Old Net}} = \frac{93}{97}$. So, New Net = $237650 \times \frac{93}{97} = 2450 \times 93 = 227850$. Common Pitfall Calculating the tax amount on the net income rather than the gross income, or misinterpreting "3 paise in a rupee" as a fixed currency amount instead of a percentage ($3\%$). Final Answer Therefore, the correct answer is **₹ 227850**.