Ms. Pooja invests $13\%$ of her monthly salary, i.e. ₹ $8554$ in Mediclaim Policies. Later she invests $23\%$ of her monthly salary on Child Education Policies ; also she invests another $8\%$ of her monthly salary on Mutual Funds. What is the total annual amount invested by Ms. Pooja?

### Concept & Formula This problem requires mapping a known percentage to a given absolute value to find the base salary, and then calculating a new cumulative percentage from that base. The timeframe (monthly vs. annual) is a crucial component of the calculation. $$ \text{Total Percentage} \times \text{Base Value} = \text{Target Value} $$ ### Step-by-Step Solution **Given:** * Investment in Mediclaim = $13\%$ of Monthly Salary (MS) = ₹ $8554$ * Investment in Child Education = $23\%$ of MS * Investment in Mutual Funds = $8\%$ of MS **Calculation:** * First, find the total percentage of the monthly salary that is invested: $$\text{Total Invested } \% = 13\% + 23\% + 8\% = 44\%$$ * Next, use the known $13\%$ valuation to find the total monthly salary: $$13\% \text{ of MS} = 8554$$ $$\frac{13}{100} \times \text{MS} = 8554$$ $$\text{MS} = \frac{8554 \times 100}{13} = 65800$$ * Calculate the total monthly investment ($44\%$ of MS): $$\text{Monthly Investment} = \frac{44}{100} \times 65800 = 28952$$ * Calculate the total **annual** investment by multiplying by $12$: $$\text{Annual Investment} = 28952 \times 12 = 347424$$ ### Exam Strategy & Shortcut To save time, bypass finding the absolute monthly salary entirely. You know $13\%$ equals $8554$. You need to find $44\%$, but annualized (multiplied by $12$). Let $I$ be the monthly investment. $$I = \left( \frac{44}{13} \right) \times 8554$$ Since $8554 \div 13 = 658$, the monthly investment is $44 \times 658$. Multiply by $12$ for the annual amount: $44 \times 658 \times 12 = 347424$. Focusing on the unit digit can quickly verify the result: $4 \times 8 \times 2 = 64$. The unit digit must be $4$. Looking at the options, only (d) ends in $4$. ### Common Pitfall The most common mistake is stopping after calculating the monthly investment (₹ $28952$) and selecting option (a). The question explicitly asks for the **total annual amount**, requiring multiplication by $12$. ### Final Answer **Therefore, the correct answer is ₹ 347424.**