Kajal invested x at a compound interest rate of 5% per annum for 2 years and 146 days. The total interest received was Rs. 9964. Calculate the principal amount (x).

Kajal invested $x$ at a compound interest rate of $5\%$ per annum for 2 years and 146 days. The total interest received was Rs. 9964.
First, convert the time into years:
$2 \text{ years and } 146 \text{ days} = 2 + \frac{146}{365} = 2 + \frac{2}{5} = 2.4 \text{ years}$.
The amount $A$ with compound interest for a fractional period is given by:

$$A = P \left(1 + \frac{R}{100}\right)^{\text{whole years}} \left(1 + \frac{R \times \text{fractional part of year}}{100}\right)$$

Substitute $P=x$, $R=5\%$, whole years $= 2$, and fractional part of year $= \frac{2}{5}$:

$$A = x \left(1 + \frac{5}{100}\right)^2 \left(1 + \frac{5}{100} \times \frac{2}{5}\right)$$ $$A = x \left(\frac{105}{100}\right)^2 \left(1 + \frac{1}{20} \times \frac{2}{5}\right)$$ $$A = x \left(\frac{21}{20}\right)^2 \left(1 + \frac{2}{100}\right)$$ $$A = x \left(\frac{441}{400}\right) \left(\frac{102}{100}\right) = x \left(\frac{441}{400}\right) \left(\frac{51}{50}\right)$$ $$A = x \frac{441 \times 51}{400 \times 50} = x \frac{22491}{20000}$$

The compound interest ($CI$) is $A - x$:

$$CI = x \frac{22491}{20000} - x = x \left(\frac{22491 - 20000}{20000}\right) = x \left(\frac{2491}{20000}\right)$$

We are given $CI = \text{Rs. } 9964$:

$$x \left(\frac{2491}{20000}\right) = 9964$$

Solve for $x$:

$$x = \frac{9964 \times 20000}{2491}$$

Recognize that $9964 = 4 \times 2491$:

$$x = 4 \times 20000 = 80000$$

The principal amount $x$ is Rs. 80,000.

Now, find the simple interest if $x$ (Rs. 80,000) is invested at $10\%$ per annum for 2 years.
Principal $P = \text{Rs. } 80000$
Rate $R = 10\%$
Time $T = 2 \text{ years}$
The formula for simple interest ($SI$) is:

$$SI = \frac{P \times R \times T}{100}$$ $$SI = \frac{80000 \times 10 \times 2}{100}$$ $$SI = 800 \times 10 \times 2$$ $$SI = 16000$$

The simple interest earned would be Rs. 16,000.

The final answer is $\text{16,000}$.