Shortcut Trick
Total interest for 1 year = 8350 ÷ 2 = ₹4175.
Assume total ₹29500 was invested in Scheme B at 15%.
Calculated interest = 29500 × 15% = ₹4425.
Difference in interest = 4425 − 4175 = ₹250.
Amount in Scheme A = Difference ÷ (Rate B − Rate A) = 250 ÷ (15% − 12.5%) = 250 ÷ 2.5% = ₹10000.
∴ The correct answer is ₹10000.
Alternate Method
Given: Total Investment = ₹29500, Rate A = 12.5%, Rate B = 15%, Total Interest (2 yrs) = ₹8350.
Formula Used: Simple Interest (S.I.) = (Principal × Rate × Time) ÷ 100
⇒ Interest if all amount in Scheme A for 2 years = (29500 × 12.5 × 2) ÷ 100 = ₹7375
⇒ Interest if all amount in Scheme B for 2 years = (29500 × 15 × 2) ÷ 100 = ₹8850
⇒ Total actual interest earned = ₹8350
⇒ By Alligation Method, Ratio of Investment (A : B) = (8850 − 8350) : (8350 − 7375)
⇒ Ratio A : B = 500 : 975 = 20 : 39
⇒ Sum of ratio parts = 20 + 39 = 59 units
⇒ 59 units = ₹29500 ⇒ 1 unit = ₹500
⇒ Amount in Scheme A = 20 × 500 = ₹10000
∴ The correct answer is ₹10000.
Additional Information
Simple Interest Concept
Simple Interest is calculated only on the Principal amount. Formula: S.I. = P × R × T ÷ 100.
Alligation in Interest
When a sum is divided into two parts at different rates, the Alligation of the interest rates or interests gives the ratio of the Principals.
Effective Rate of Interest
Overall Rate % = (Total Interest ÷ Total Principal) × (100 ÷ Time). This helps find the weighted average of multiple schemes.