Out of Rs. 8000, Gopal invested a certain sum in scheme A and the remaining sum in scheme B for two years. Both the schemes offer compound interest (compunded annually). The rate of interest of scheme A and B are 10 p.c.p.a. and 20 p.c.p.a. respectively. If the total amount accrued by him after two years from both the schemes together was Rs. 10,600, what was the amount invested in scheme B ?

Let the amount invested in scheme B = $$Rs. x$$

=> Amount invested in scheme A = $$Rs. (8,000 - x)$$

The rate of interest of scheme A and B are 10 p.c.p.a. and 20 p.c.p.a. respectively

Also, amount under C.I. = $$P (1 + \frac{R}{100})^T$$

=> $$[x (1 + \frac{10}{100})^2] + [(8000 - x) (1 + \frac{20}{100})^2] = 10,600$$

=> $$x (\frac{11}{10})^2 + (8000 - x) (\frac{6}{5})^2 = 10600$$

=> $$\frac{121 x}{100} + 11520 - \frac{36 x}{25} = 10600$$

=> $$\frac{23 x}{100} = 11520 - 10600 = 920$$

=> $$x = 920 \times \frac{100}{23} = 40 \times 100$$

=> $$x = Rs. 4,000$$