Question : A man invested INR 4,500 at 5% per annum and INR 5,500 at 8% per annum simple interest. Both investments were for 4 years each. The amount received from the lower rate of interest is what percent (rounded off to the nearest integer) of the amount received from the higher rate of interest?
Option 1: 63%
Option 2: 74%
Option 3: 51%
Option 4: 48%
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Correct Answer: 74%
Solution :
A man invested Rs. 4,500 at 5% per annum and Rs. 5,500 at 8% per annum simple interest.
For the first investment,
Time = 4 years
Principal = Rs. 4,500
Rate = 5% per annum
Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$ = $\frac{4500 \times 4 \times 5}{100}$ = Rs. 900
Amount = Rs. 4500 + Rs. 900 = Rs. 5400
For the second investment,
Time = 4 years
Principal = Rs. 5,500
Rate = 8% per annum
Simple interest = $\frac{5500 \times 4 \times 8}{100}$ = Rs. 1,760
Amount = Rs. 5,500 + Rs. 1,760 = Rs. 7,260
The amount received from a lower rate of interest = Rs. 5,400
Required percentage = $\frac{5400}{7260} \times 100$ = 74.38 ≈ 74%
Hence, the correct answer is 74%.
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