Asmita invests an amount of ₹ 9534 @ 4 p.c.p.a. to obtain a total amount of ₹ 11442 on simple interest after a certain period. For how many years did she invest the amount to obtain the total sum?

### Concept & Simple Interest Time Formula The Simple Interest ($SI$) is the difference between the Final Amount ($A$) and the Principal ($P$). The formula for time ($T$) when $SI$, Principal, and Rate ($R$) are known is: $$T = \frac{SI \times 100}{P \times R}$$ ### Step-by-Step Solution * Given Principal, $P = \text{₹ } 9534$ * Given Amount, $A = \text{₹ } 11442$ * Given Rate, $R = 4\%$ p.a. * First, find the Simple Interest: $SI = A - P = 11442 - 9534 = \text{₹ } 1908$ * Now, apply the time formula: $T = \frac{1908 \times 100}{9534 \times 4}$ $T = \frac{190800}{38136} = 5 \text{ years}$ ### Exam Strategy & Shortcut To quickly check the division, observe the final digits or do a rough estimation: $9500 \times 4\% = 380$ per year. Total interest is about $1900$. $1900 / 380 = 5$ exactly. ### Common Pitfall A common error is to directly plug the Final Amount ($11442$) into the formula instead of the Simple Interest ($1908$), leading to completely incorrect calculations. ### Final Answer Therefore, the correct answer is **5 years**.