In aptitude (Simple Interest), Dev lends ₹8,000 to Jairam for 17 years and ₹4,700 to Karnik for 16 years at the same simple interest rate. If Dev receives a total interest of ₹21,120 from both loans together, what is the annual rate of interest (in % per annum)?

Introduction / Context:
This problem combines simple interest from two separate loans given at the same rate but for different principals and time periods. You are asked to find the common rate of interest from the total interest received. Such questions are common in banking aptitude sections and test your ability to set up equations that combine multiple simple interest amounts.

Given Data / Assumptions:

• Loan 1: Principal P1 = ₹8,000, time t1 = 17 years.
• Loan 2: Principal P2 = ₹4,700, time t2 = 16 years.
• Common rate of interest = r% per annum (simple interest).
• Total interest received from both loans = ₹21,120.
• We must find r in percent per annum.

Concept / Approach:
Under simple interest, interest on one loan is: SI1 = (P1 * r * t1) / 100. Similarly, interest on the second loan is: SI2 = (P2 * r * t2) / 100. Total interest is the sum: SI_total = SI1 + SI2. Because r is the same for both, we can factor it out: SI_total = (r / 100) * (P1 * t1 + P2 * t2). We know SI_total and the principals and times, so we can compute the combined term and solve for r.

Step-by-Step Solution:
Step 1: Compute P1 * t1 = 8,000 * 17 = 136,000. Step 2: Compute P2 * t2 = 4,700 * 16 = 75,200. Step 3: Add these to obtain P1 * t1 + P2 * t2 = 136,000 + 75,200 = 211,200. Step 4: Use the formula SI_total = (r / 100) * (P1 * t1 + P2 * t2). Step 5: Substitute SI_total = 21,120: 21,120 = (r / 100) * 211,200. Step 6: Rearrange for r: r = (21,120 * 100) / 211,200. Step 7: Simplify the fraction: 21,120 * 100 / 211,200 = 2,112,000 / 211,200 = 10. Step 8: Therefore, r = 10% per annum.

Verification / Alternative check:
We can verify by computing the individual interests at r = 10%. Loan 1: SI1 = (8,000 * 10 * 17) / 100 = (8,000 * 170) / 100 = 1,360,000 / 100 = 13,600. Loan 2: SI2 = (4,700 * 10 * 16) / 100 = (4,700 * 160) / 100 = 752,000 / 100 = 7,520. Total interest: SI_total = 13,600 + 7,520 = 21,120. This matches the given total, confirming that the rate is 10% per annum.

Why Other Options Are Wrong:
10.5%, 11%, 11.5%, and 9.5% all produce total interest amounts larger or smaller than ₹21,120 when substituted into the formula. Only 10% results in the exact total interest given in the question, so the other rates must be rejected.

Common Pitfalls:
A common error is to calculate each simple interest separately but make arithmetic mistakes when multiplying or adding large numbers. Another mistake is to average the time periods or principals incorrectly instead of using the combined expression. Keeping the formula in the factored form (r / 100) * (sum of P * t) helps organize the work and reduces the risk of error.

Final Answer:
The annual simple interest rate that makes the total interest from both loans equal to ₹21,120 is 10% per annum.