Shortcut Trick
Effective interest rate for Case 1 = 9% × 2.5 years = 22.5%
Total amount percentage = 100% (Principal) + 22.5% = 122.5%
Given, 122.5% → ₹11760 ⇒ 1% → 11760 ÷ 122.5 = ₹96
Required Simple Interest for Case 2 = 15% × 4.4 years = 66%
Total Simple Interest = 66 × 96 = ₹6336
∴ The correct answer is ₹6336.
Alternate Method
Given: Amount (A1) = ₹11760, Rate (R1) = 9%, Time (T1) = 2.5 years, Rate (R2) = 15%, Time (T2) = 4.4 years.
Formula Used: SI = (P × R × T) / 100 | Amount = P + SI
⇒ Amount1 = P + (P × 9 × 2.5) / 100
⇒ 11760 = P + (P × 22.5) / 100
⇒ 11760 = P(1 + 0.225) ⇒ 11760 = 1.225P
⇒ P = 11760 ÷ 1.225 = 9600
⇒ SI2 = (9600 × 15 × 4.4) / 100
⇒ SI2 = 96 × 66 = 6336
∴ The correct answer is ₹6336.
Additional Information
Simple Interest Constant Property
Simple Interest remains constant for every year if the principal and rate are unchanged. SI = Principal × Rate × Time / 100.
Effective Rate of Interest
For Simple Interest, the effective rate for a period is the product of the annual rate and the time in years (R × T).
Amount in Simple Interest
The total amount (A) is the sum of the principal (P) and interest (SI). A = P(1 + RT/100).