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-by-Step Explanation:

1. Define the Variables:
Let the total sum available for investment be Rs. 40,000.
Let the sum invested in Account B be $x$.
Therefore, the remaining sum invested in Account A is $(40000-x)$.

2. Calculate Simple Interest from Account A:
Account A offers simple interest at a rate of 30% per annum for 3 years.
The formula for Simple Interest (SI) is:

$\text{SI}=\frac{P\times R\times T}{100}$

Substituting the values for Account A:
Principal ($P$) = $40000-x$
Rate ($R$) = 30% per annum
Time ($T$) = 3 years

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

$\text{SI}=\frac{(40000-x)\times 90}{100}$

$\text{SI}=0.9\times (40000-x)$

$\text{SI}=36000-0.9x$

3. Calculate Compound Interest from Account B:
Account B yields interest at 20% per annum compounded annually for 3 years.
The formula for Compound Interest (CI) is:

$\text{CI}=P\times \left[{\left(1+\frac{R}{100}\right)}^T-1\right]$

Substituting the values for Account B:
Principal ($P$) = $x$
Rate ($R$) = 20%
Time ($T$) = 3 years

$\text{CI}=x\times \left[{\left(1+\frac{20}{100}\right)}^3-1\right]$

$\text{CI}=x\times \left[{\left(1.2\right)}^3-1\right]$

$\text{CI}=x\times \left[1.728-1\right]$

$\text{CI}=0.728x$

4. Set up and Solve the Equation:
The problem states that the interest accrued from Account A is Rs. 9952 more than the interest accrued from Account B:

$\text{SI}-\text{CI}=9952$

Substituting the expressions derived for SI and CI:

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

$36000-1.628x=9952$

$1.628x=36000-9952$

$1.628x=26048$

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

$x=16000$

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