Question

the difference between compound interest and simple interest on a certain sum for 2 years at 7.5% per annum is rupees 3600 find the sum

Answer 1

$si = \frac{p \times 7.5 \times 2}{100} = \frac{15p}{100} = \frac{3p}{20} \\ ci = p {(1 + \frac{7.5}{100}) }^{2} - p = p {(1 + \frac{3}{40}) }^{2} - p \\ \: \: \: \: \: = p {( \frac{43}{40}) }^{2} - p \\given \: ci - si = 3600 \\ p( \frac{1849}{1600} ) - p - \frac{3p}{20} = 3600 \\ p( \frac{1849 - 1600 - 240}{1600} ) = 3600 \\ p = \frac{3600 \times 1600}{1849 - 1840} = \frac{3600 \times 1600}{9} \\ \: \: \: \: = 400 \times \times 1600 = 640000$