If simple interest on ₹ 600 for 4 years and on ₹ 600 for 2 years combined together is ₹ 180, find the rate of interest.

### Concept & Additive Property of Simple Interest When the principal and rate are the same, the simple interest earned over different periods can be calculated by combining the time periods. $$SI_{total} = \frac{P \times R \times (T_1 + T_2)}{100}$$ ### Step-by-Step Solution * Given Principal, $P = \text{₹ } 600$ * Given Total Simple Interest, $SI = \text{₹ } 180$ * Given Time periods, $T_1 = 4 \text{ years}$ and $T_2 = 2 \text{ years}$ * Total effective time = $4 + 2 = 6 \text{ years}$. * Apply the formula: $180 = \frac{600 \times R \times 6}{100}$ $180 = 36 \times R$ $R = \frac{180}{36} = 5\%$ ### Exam Strategy & Shortcut Instead of computing two separate equations ($\frac{600 \times 4 \times R}{100} + \frac{600 \times 2 \times R}{100} = 180$), realize that earning interest on ₹ 600 for 4 years and then for another 2 years is perfectly identical to earning interest on ₹ 600 for 6 years straight. $600 \times 6\% \text{ of } R = 36R = 180 \rightarrow R=5$. ### Common Pitfall Creating overly complex equations for each part independently can waste valuable time and increase the chance of algebraic errors. ### Final Answer Therefore, the correct answer is **5%**.