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Rashmita invests 20% of her Principal at 15% per annum for 4 years, 50% of the remaining at 20% per annum for 2 years and the rest at 12% per annum of 1 year at simple interest. If the interest is calculated on the whole sum, then find the rate of interest per annum.
1. 22.8%
2. 32.8%
3. 33.8%
4. 42.8%
5. None of these

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Best answer
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%.

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