Choose the correct option to solve the problem.
An investor has a total of Rs. 40000. He allocates a portion of this sum to Account A, which yields 30% per annum simple interest, and the remainder to Account B, which earns 20% interest compounded annually. If, after three years, the total interest generated from Account A is Rs. 9952 more than the interest accrued from Account B, find the sum invested in Account B.

The correct option is Rs.16000.

Step 1: Understand the given information and define the variables.
Total sum invested = Rs. 40000.
Let the sum invested in Account B be $x$.
Therefore, the sum invested in Account A is $(40000-x)$.

Step 2: Calculate the Simple Interest earned from Account A.
Account A offers a 30% per annum simple interest for a period of 3 years.
The formula for Simple Interest is:

$\text{Simple Interest}=\frac{\text{Principal}\times \text{Rate}\times \text{Time}}{100}$

Substituting the values for Account A:

${\text{Interest}}_{\text{A}}=\frac{(40000-x)\times 30\times 3}{100}$

${\text{Interest}}_{\text{A}}=\frac{(40000-x)\times 90}{100}=0.9(40000-x)$

${\text{Interest}}_{\text{A}}=36000-0.9x$

Step 3: Calculate the Compound Interest earned from Account B.
Account B earns 20% interest compounded annually for 3 years.
The formula for the total amount under Compound Interest is:

$\text{Amount}=\text{Principal}{(1+\frac{\text{Rate}}{100})}^{\text{Time}}$

Substituting the values for Account B:

${\text{Amount}}_{\text{B}}=x{(1+\frac{20}{100})}^3=x{\left(1.2\right)}^3=1.728x$

The Compound Interest is calculated by subtracting the principal from the total amount:

${\text{Interest}}_{\text{B}}=1.728x-x=0.728x$

Step 4: Set up the equation and solve for $x$.
We are given that the interest generated from Account A is Rs. 9952 more than the interest accrued from Account B:

${\text{Interest}}_{\text{A}}-{\text{Interest}}_{\text{B}}=9952$

Substitute the expressions obtained in Step 2 and Step 3:

$(36000-0.9x)-0.728x=9952$

$36000-1.628x=9952$

$1.628x=36000-9952$

$1.628x=26048$

$x=\frac{26048}{1.628}$

$x=16000$

Hence, the sum invested in Account B is Rs. 16000.