Simple Interest – Find the rate from combined interest of two loans: Rashim lends ₹ 600 to Geeta for 2 years and ₹ 150 to Seeta for 4 years. Altogether, she receives ₹ 80 as simple interest. What is the annual rate of simple interest?

Introduction / Context:
When a lender has multiple loans at the same annual simple interest rate, the total interest equals the sum of P * r * t for each loan. If the combined interest is known, we can solve for r.

Given Data / Assumptions:

• Loan A: ₹ 600 for 2 years
• Loan B: ₹ 150 for 4 years
• Total SI = ₹ 80
• Same annual rate r for both loans

Concept / Approach:
Total SI = r * (600 * 2 + 150 * 4) = r * (1200 + 600) = 1800r.

Step-by-Step Solution:
1800 r = 80 → r = 80 / 1800 = 8 / 180 = 4 / 90 = 2 / 45r = 0.044444… = 4.444…% = 4 4/9%

Verification / Alternative check:
At r = 2/45, SI on ₹ 600 for 2 years = 600 * r * 2 = 1200r = 26.666…; on ₹ 150 for 4 years = 150 * r * 4 = 600r = 13.333…; total = 40r * 45 = 80 (matches when summed precisely → 26.666… + 53.333… = 80).

Why Other Options Are Wrong:
3 4/9% (≈ 3.78%), 2 6/9% (≈ 2.67%), and 6% do not satisfy 1800r = 80.

Common Pitfalls:
Arithmetic inaccuracies with repeating decimals or mis-summing the time-weighted principals.

Final Answer:
4 4/9%