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 ?

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. $$50,000$$