
Shortcut Trick
Total interest for 2 years = ₹4,820 ⇒ Interest for 1 year = ₹2,410.
Overall interest rate = (2,410 ÷ 31,000) × 100 = 241/31%.
Using Alligation: (9% − 241/31%) : (241/31% − 7%) = 38/31 : 24/31 = 19 : 12.
Sum at 9% = (12 ÷ 31) × 31,000 = ₹12,000.
∴ The correct answer is ₹12000.

Alternate Method
Given: Total Sum = ₹31,000, Total Interest = ₹4,820, Time = 2 years.
Formula Used: Simple Interest (SI) = (P × R × T) ÷ 100

⇒ Let the sum lent at 9% be x and at 7% be (31,000 − x).
⇒ Interest from first part = (x × 9 × 2) ÷ 100 = 0.18x
⇒ Interest from second part = ((31,000 − x) × 7 × 2) ÷ 100 = 0.14 × (31,000 − x)
⇒ 0.18x + 4,340 − 0.14x = 4,820
⇒ 0.04x = 4,820 − 4,340
⇒ 0.04x = 480
⇒ x = 480 ÷ 0.04 = 12,000
∴ The correct answer is ₹12000.

Additional Information
Simple Interest vs Compound Interest
Simple Interest is calculated only on the principal amount, whereas Compound Interest is calculated on the principal plus accumulated interest.
Alligation Method in SI
When a sum is divided into two parts with different interest rates, the ratio of the two parts can be found using the alligation of their respective rates against the average rate.
Effective Rate of Interest
Effective Rate = (Total Interest ÷ Total Principal) × (100 ÷ Time). This helps in comparing different investment schemes directly.