Shortcut Trick
Total Interest % for 4 years: Lower rate = 5% × 4 = 20% | Higher rate = 8% × 4 = 32%.
Amount 1 (Lower) = 4500 × 120% = 5400.
Amount 2 (Higher) = 5500 × 132% = 7260.
Required % = (5400 ÷ 7260) × 100 ≈ 74%.
∴ The correct answer is 74%.
Alternate Method
Given:
Case 1: Principal (P1) = ₹4,500, Rate (R1) = 5%, Time (T) = 4 years.
Case 2: Principal (P2) = ₹5,500, Rate (R2) = 8%, Time (T) = 4 years.
Formula Used:
Simple Interest (SI) = (P × R × T) ÷ 100
Amount (A) = P + SI
Calculations:
⇒ SI1 = (4500 × 5 × 4) ÷ 100 = 900
⇒ Amount1 (lower rate) = 4500 + 900 = ₹5,400
⇒ SI2 = (5500 × 8 × 4) ÷ 100 = 1760
⇒ Amount2 (higher rate) = 5500 + 1760 = ₹7,260
⇒ Required Percentage = (5400 ÷ 7260) × 100
⇒ Required Percentage = 54000 ÷ 726 ≈ 74.38%
⇒ Rounded off to the nearest integer = 74%
∴ The correct answer is 74%.
Additional Information
Simple Interest Concept
Interest is calculated only on the initial Principal amount for every year. SI = (P × R × T) ÷ 100.
Amount in Simple Interest
The total Amount (A) received at the end of the period is the sum of Principal and Interest: A = P(1 + RT/100).
Effective Rate of Interest
The total interest earned can be expressed as a single effective percentage of the principal, which is (Rate × Time)%.