Question : If a sum of money becomes INR 6,000 in 3 years and INR 10,500 in 7 years and 6 months at the same rate of simple interest, then what is the rate of interest?
Option 1: $33 \frac{1}{3}$%
Option 2: $25 \frac{1}{2}$%
Option 3: $45 \frac{2}{3}$%
Option 4: $66 \frac{1}{3}$%
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Correct Answer: $33 \frac{1}{3}$%
Solution : Given: A sum of money becomes INR 6,000 in 3 years and INR 10,500 in 7 years and 6 months at the same rate of simple interest. The difference between the two sums is the interest earned for the period. Interest earned for 4 years 6 months = 10500 – 6000 = INR 4,500 Interest earned for 1 year = $\frac{4500}{4.5}$ = INR 1,000 Interest earned for 3 years = 1000 × 3 = INR 3,000 Principal = Sum – Interest for 3 years ⇒ Principal = 6000 – 3000 = INR 3,000 Simple Interest $=\frac{\text{Principal×Rate×Time}}{100}$ ⇒ $3000 = \frac{3000×\text{Rate}×3}{100} $ ⇒ Rate $=\frac{100}{3}$% ⇒ Rate $=33\frac{1}{3}$% So, the rate of interest is $33\frac{1}{3}$%. Hence, the correct answer is $33\frac{1}{3}$%.
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