Question : If the simple interest at the same rate of interest on INR 500 for 4 years and INR 700 for 2 years combined, is INR 280, then what is the rate of interest?
Option 1: $9 \frac{3}{17}\%$
Option 2: $6 \frac{5}{17}\%$
Option 3: $8 \frac{4}{17}\%$
Option 4: $7 \frac{3}{17}\%$
Correct Answer: $8 \frac{4}{17}\%$
Solution :
P = INR 500 and INR 700
T = 4 years and 2 years
R = same for both
According to the question,
$280 = \frac{\text{500×R×4}}{100}$+$\frac{\text{700×R×2}}{100}$
⇒ $280 = \frac{\text{2000R}}{100}$+$\frac{\text{1400R}}{100}$
⇒ $ 280 = \frac{\text{3400R}}{100}$
⇒ $R = \frac{280}{34} = 8\frac{4}{17}$
Hence, the correct answer is $8 \frac{4}{17}\%$.
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