A person lends Rs. 10000 to B for 3 years and Rs. 6000 to C for 4 years, both at the same annual simple interest rate. If the total interest received from B and C together is Rs. 5400 over these periods, what is the common rate of interest per annum in percent?

Introduction / Context:
This is a straightforward simple interest problem that often appears in aptitude exams. A lender gives different amounts to two borrowers for different time periods, but at the same simple interest rate. The total interest from both loans is known, and we need to find the common rate of interest per annum. The question checks whether you can correctly set up and solve a linear equation using the basic simple interest formula.

Given Data / Assumptions:

• Loan to B: Principal P₁ = Rs. 10000 for 3 years.
• Loan to C: Principal P₂ = Rs. 6000 for 4 years.
• Rate of simple interest is r percent per annum for both loans.
• Total interest from B and C together over the entire time is Rs. 5400.
• Interest is simple interest in both cases, not compound interest.

Concept / Approach:
For simple interest, the formula is:
Simple interest = (Principal * Rate * Time) / 100.
We will calculate the interest from each borrower separately in terms of r, then add them to match the given total interest of Rs. 5400. This will give us a single linear equation in r. Solving that equation will directly provide the annual rate of interest in percent. Because both loans are at the same rate, we can combine the terms neatly.

Step-by-Step Solution:
Step 1: Let the common rate of interest be r percent per annum. Step 2: Interest from B = (P₁ * r * t₁) / 100 = (10000 * r * 3) / 100. Step 3: Simplify B's interest: (10000 * 3 / 100) * r = 300 * r. Step 4: Interest from C = (P₂ * r * t₂) / 100 = (6000 * r * 4) / 100. Step 5: Simplify C's interest: (6000 * 4 / 100) * r = 240 * r. Step 6: Total interest from both loans = 300r + 240r = 540r. Step 7: We are told that this total interest equals Rs. 5400, so 540r = 5400. Step 8: Divide both sides by 540 to get r = 5400 / 540 = 10. Step 9: Therefore, the rate of simple interest is 10 percent per annum.

Verification / Alternative check:
We can quickly verify the answer by substituting r = 10 percent back into the calculations. Interest from B becomes (10000 * 10 * 3) / 100 = 3000. Interest from C becomes (6000 * 10 * 4) / 100 = 2400. Adding both, 3000 + 2400 = 5400, which exactly matches the total interest given in the problem. Thus, the computed rate is consistent with all given data.

Why Other Options Are Wrong:
At 12 % or 15 %, the total interest would exceed Rs. 5400, giving values higher than the target amount. At 20 % or 25 %, the interest amounts become even larger and clearly unrealistic compared with the stated total. Only 10 % produces exactly Rs. 5400 when the interest from both loans is combined, so the other options do not satisfy the equation 540r = 5400.

Common Pitfalls:
One common mistake is to average the time periods or principals incorrectly instead of using the formula on each loan separately. Another error is to forget to divide by 100 when applying the simple interest formula, which leads to very large or very small rates. Some students also miscalculate the combined coefficient (300 + 240) and set up the wrong equation. Being systematic about writing each interest term and then combining them avoids these errors.

Final Answer:
The common annual simple interest rate that makes the total interest from both loans equal to Rs. 5400 is 10 % per annum.