Nupur invests ₹ $89856$, which is $26\%$ of her annual income, in mutual funds. What is her monthly income?

### Concept & Formula This problem links an absolute investment amount to a percentage of an annual income, but requires the monthly income as the final answer. Converting between annual and monthly figures is the key algebraic step. $$ \text{Percentage} \times \text{Base Income} = \text{Investment Amount} $$ ### Step-by-Step Solution **Given:** * Investment amount = ₹ $89856$ * Percentage of annual income = $26\%$ **Calculation:** * Let the Annual Income be $A$. $$26\% \text{ of } A = 89856$$ $$\frac{26}{100} \times A = 89856$$ * Solve for Annual Income $A$: $$A = \frac{89856 \times 100}{26}$$ $$A = 3456 \times 100 = 345600$$ * The question asks for the **monthly** income. Divide the annual income by $12$: $$\text{Monthly Income} = \frac{345600}{12} = 28800$$ ### Exam Strategy & Shortcut Calculate the monthly component directly in one equation to minimize large number division. Let Monthly Income be $M$. The Annual Income is $12M$. $$26\% \text{ of } (12M) = 89856$$ $$12M = \frac{89856}{0.26}$$ $$M = \frac{89856}{12 \times 0.26} = \frac{7488}{0.26}$$ $$M = \frac{748800}{26} = 28800$$ By dividing by $12$ early on ($89856 \div 12 = 7488$), the numbers stay much smaller and easier to manage during calculation. ### Common Pitfall A common pitfall is successfully calculating the total annual income (₹ $345600$) but forgetting to divide by $12$ at the end because the word "annual" was prominent at the start of the problem statement. ### Final Answer **Therefore, the correct answer is ₹ 28800.**