A sum amounts to ₹ 9075 in $$1\frac{1}{3}$$​ years at 15% p.a, interest compounded 8-monthly. What is the simple interest (in ₹) on the same sum for the same period and at the same rate of interest ?

Correct option is B

​$$\textbf{Given :} \\\ \, \\A = 9075,\ R = 15\%\ \text{p.a.},\ T = 1\frac{1}{3} = \frac{4}{3}\ \text{years} \\\ \, \\\text{Compounded 8-monthly} \\\ \, \\\textbf{Formula Used :} \\\ \, \\A = P\left(1+\frac{R}{100}\right)^n \\\ \, \\\text{SI} = \frac{P \times R \times T}{100} \\\ \, \\\textbf{Solution :} \\\ \, \\8\ \text{months} = \frac{2}{3}\ \text{year} \\\ \, \\n = \frac{\frac{4}{3}}{\frac{2}{3}} = 2 \\\ \, \\\text{Rate per period} = 15 \times \frac{2}{3} = 10\% \\\ \, \\9075 = P(1.1)^2 \\\ \, \\9075 = 1.21P \\\ \, \\P = 7500 \\\ \, \\\text{SI} = \frac{7500 \times 15 \times \frac{4}{3}}{100} = 1500 \\\ \, \\\textbf{Final Answer :} \\\ \, \\₹1500$$​​