A person lends ₹5,000 to B for 2 years and ₹3,000 to C for 4 years at the same annual rate of simple interest. If the total interest received from both borrowers together is ₹2,200, what is the rate of simple interest per annum?

Introduction:
This problem checks whether you can combine simple interest from multiple loans when the interest rate is the same. Since simple interest adds linearly, total interest is the sum of the interests on each loan. We form one equation in the unknown rate and solve it.

Given Data / Assumptions:

• Loan 1: P1 = ₹5,000, t1 = 2 years
• Loan 2: P2 = ₹3,000, t2 = 4 years
• Same rate r% per annum for both loans
• Total simple interest received = ₹2,200
• Formula: SI = (P * r * t) / 100

Concept / Approach:
Compute interest from each loan in terms of r, add them, and set the sum equal to ₹2,200. This produces a single linear equation in r because all other quantities are known.

Step-by-Step Solution:
Interest from B: SI1 = (5000 * r * 2) / 100 SI1 = (10000r) / 100 = 100r Interest from C: SI2 = (3000 * r * 4) / 100 SI2 = (12000r) / 100 = 120r Total interest: SI1 + SI2 = 100r + 120r = 220r Given total interest = 2200, so 220r = 2200 r = 2200 / 220 = 10

Verification / Alternative check:
Notice that total interest equals r times (5000*2 + 3000*4)/100. The combined principal-time is 10000 + 12000 = 22000, so interest is (22000*r)/100 = 220r, matching the derivation.

Why Other Options Are Wrong:
5% and 7% produce total interest less than ₹2,200. 12% produces more than ₹2,200. 7.5% and similar values are plausible but do not satisfy the exact total interest equation.

Common Pitfalls:
Adding principals directly without weighting by time, forgetting to divide by 100 in the simple interest formula, or mistakenly compounding interest.

Final Answer:
The required simple interest rate is 10% per annum.