Calculate the principal amount (x) using the compound interest information.

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:
$2 \text{ years and } 146 \text{ days} = 2 + \frac{146}{365} \text{ years}$.
Since $146 = 2 \times 73$ and $365 = 5 \times 73$, we have $\frac{146}{365} = \frac{2}{5} = 0.4$ years.
So, the total time is 2.4 years.

For compound interest with a fractional period, the amount $A$ is calculated as:

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

Here, $P = x$, $R = 5\%$, whole years $= 2$, and fractional part of year $= \frac{146}{365}$.

$$A = x \left(1 + \frac{5}{100}\right)^2 \left(1 + \frac{5}{100} \times \frac{146}{365}\right)$$ $$A = x \left(\frac{105}{100}\right)^2 \left(1 + \frac{1}{20} \times \frac{2}{5}\right)$$ $$A = x \left(\frac{21}{20}\right)^2 \left(1 + \frac{2}{100}\right)$$ $$A = x \left(\frac{441}{400}\right) \left(1 + \frac{1}{50}\right)$$ $$A = x \left(\frac{441}{400}\right) \left(\frac{51}{50}\right)$$ $$A = x \frac{441 \times 51}{400 \times 50} = x \frac{22491}{20000}$$

The compound interest ($CI$) is $A - P$. We are given that $CI = \text{Rs. } 9964$.

$$CI = x \frac{22491}{20000} - x = 9964$$ $$x \left(\frac{22491 - 20000}{20000}\right) = 9964$$ $$x \left(\frac{2491}{20000}\right) = 9964$$ $$x = \frac{9964 \times 20000}{2491}$$

Since $9964 \div 2491 = 4$:

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

So, the principal amount $x$ is Rs. 80,000.

Now, we need to find how much interest Kajal could earn if she invested $x$ amount (Rs. 80,000) on simple interest 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:

$$SI = \frac{P \times R \times T}{100}$$ $$SI = \frac{80000 \times 10 \times 2}{100}$$ $$SI = 800 \times 10 \times 2$$ $$SI = 8000 \times 2$$ $$SI = 16000$$

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

Comparing this with the given options:

(a) 16,000

(b) 15,000

(c) 14,000

(d) 20,000

The correct option is (a).

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