A certain amount is invested in scheme A for 6 years which offers simple interest at the rate of x% per annum. The same amount is invested in scheme B for 2 years which offers compound interest compounded annually at the rate of 10% per annum. Interest earned from scheme A is twice of that earned in scheme B. If the rate of interest of scheme A had been (x+2)% per annum, the difference between the interests after corresponding periods would have been $3960. What is the amount invested in each scheme?
Problem: I am getting the answer to be 12000. While the book says the answer is 33000
My Attempt:
$$\frac{P*x*6}{100}=\frac{P*21}{100}*2$$
$$x=7$$ ATQ: $$\frac{54P}{100}-\frac{21P}{100}=3960$$
$$P=12000$$
If the interest in Scheme A had been $x \%$, then it would have been $ \$3960$ less than what the interest would have been if rate was $(x+2)\%$.
So, your equation must be $$\frac{54 \rm P}{100 }-\frac{42 \rm P}{100}=3960 \implies \rm P=33,000$$