Abhijit invested a certain sum at simple interest in a company X at the rate of 15% per annum. He invested the total amount received after two years from company X in another company Y at compound interest for two years at the rate of 12% per annum compounded annually. He received Rs. 81536 at the end of two years. What sum did he invest in company X in the beginning ?

Explanation

Let amount invested in company X = Rs. $$100x$$ => S.I. = $$\frac{Principal \times Rate \times Time}{100}$$ = $$\frac{100x \times 15 \times 2}{100} = 30x$$ $$\therefore$$ Amount invested in company Y = $$100x + 30x$$ = Rs. $$130x$$ $$\therefore A = P (1 + \frac{R}{100})^T$$ => $$81536 = 130x (1 + \frac{12}{100})^2$$ => $$81536 = 130x \times \frac{28}{25} \times \frac{28}{25}$$ => $$x = \frac{81536 \times 25 \times 25}{130 \times 28 \times 28}$$ => $$x = 500$$ $$\therefore$$ Amount invested in company X in the beginning = $$100 \times 500$$ = Rs. $$50,000$$