A certain sum was invested at simple interest at a certain rate for 10 years. Had it been invested at a rate 5% per annum higher, it would have earned Rs. 600 more as interest over the same period. What was the sum invested (in rupees)?

Introduction / Context:This is another reverse simple interest question where we know the extra interest earned due to an increase in the rate, and we must find the principal. Because the time period is fixed at 10 years, the additional interest is directly proportional to the principal and the increase in rate.Given Data / Assumptions:

• Time (T) = 10 years
• Increase in rate = 5% per annum
• Extra simple interest due to higher rate = Rs. 600
• We must find the principal (P)

Concept / Approach:Let the original rate be r%. At the higher rate, the rate becomes r + 5 percent. The extra interest is generated only by this extra 5%. The formula for extra simple interest is:Extra SI = (P * Increase in rate * Time) / 100We substitute the given values and solve directly for P.Step-by-Step Solution:Increase in rate = 5%Time = 10 yearsExtra SI = Rs. 600Using formula: 600 = (P * 5 * 10) / 100600 = (50P) / 100600 = P / 2So P = 600 * 2 = 1200Therefore, the sum invested is Rs. 1,200Verification / Alternative check:With a principal of Rs. 1,200, extra interest per year at 5% is:(1200 * 5) / 100 = Rs. 60Over 10 years, extra interest = 60 * 10 = Rs. 600, which matches the given extra interest. This confirms that the principal is correctly found.Why Other Options Are Wrong:If P were Rs. 1,300, extra interest would be (1300 * 5 * 10) / 100 = Rs. 650. For Rs. 1,400, extra interest would be Rs. 700, and for Rs. 1,500 it would be Rs. 750. None of these match the required extra interest of Rs. 600.Common Pitfalls:Sometimes candidates forget that the extra interest is due only to the increase in rate, not the entire rate. Others misplace the 100 in the denominator or incorrectly divide during the final step, leading to incorrect principal values. Always write the formula clearly and simplify step by step.Final Answer:The principal invested was Rs. 1,200.