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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