A) Define compound depreciation.

$$\text{Depreciation in 1st year} = P \times \frac{R}{100}$$ $$\text{Depreciation in 1st year} = 50,000 \times \frac{20}{100}$$ $$\text{Depreciation in 1st year} = 50,000 \times 0.20$$ $$\text{Depreciation in 1st year} = 10,000$$

The price depreciated in the first year is Rs. 10,000.
The final answer is $\boxed{\text{Rs. 10,000}}$.

$$V_T = P \left(1 - \frac{R}{100}\right)^T$$ $$V_3 = 50,000 \left(1 - \frac{20}{100}\right)^3$$ $$V_3 = 50,000 \left(1 - 0.2\right)^3$$ $$V_3 = 50,000 \left(0.8\right)^3$$ $$V_3 = 50,000 \times 0.512$$ $$V_3 = 25,600$$

The value of the machine after 3 years is Rs. 25,600.

$$\text{Half of current price} = \frac{50,000}{2} = 25,000$$

Half of the current price is Rs. 25,000.

Since $V_3 = \text{Rs. } 25,600$ and half of the current price is $\text{Rs. } 25,000$, we have:

$$25,600 > 25,000$$

The value of the machine after 3 years (Rs. 25,600) is greater than half of its current price (Rs. 25,000).

Conclusion:
No, it will not be possible to buy that machine at half of its current price after 3 years.
The final answer is $\boxed{\text{No, because the value after 3 years is Rs. 25,600, which is greater than half the current price of Rs. 25,000.}}$.