Correct Answer - Option 2 : 32.8%
Given:
Rashmita invests 20% of her Principal at 15% for 4 years
After that, 50% of the remaining at 20% for 2 years
And, the rest at 12% for 1 year
Formula used:
S.I = PRT/100
Where P = Principal
R = rate of interest
T = time period
Calculation:
Let the Principal be 100x
Now, 20% of the Principal = 100x × (20/100) = 20x
As per the question 20x is invested at 15% per annum for 4 years
So, the S.I = {(20x × 15 × 4)/100 = 12x
The, remaining amount = (100x - 20x) = 80x
According to the question, 50% of the remaining, i.e., 80x is invested at 20% per annum for 2 years
So, the S.I = {(80x × 50/100) × 20 × 2}/100 = 16x
Now, the rest amount = {100x - (20x + 40x)} = 40x
Now, again, according to the question, 40x is invested at 12% per annum for 1 year
So, the S.I = (40x × 12)/100 = 4.8x
The total S.I = (12x + 16x + 4.8x) = 32.8x
Let the rate of interest be R
As per the formula, we can say,
32.8x = (100x × R × 1)/100
⇒ 32.8x = Rx
⇒ R = 32.8%
∴ The rate of interest on the Principal is 32.8%.