To solve this problem, we need to first calculate the initial ratio of bronze to copper in the alloy. Then, we can determine how much of the mixture should be drawn out and replaced with bronze in order to reverse the ratio.

Let's assume that the initial quantity of the alloy is x parts. Therefore, the alloy contains 4/10 * x parts of bronze and 6/10 * x parts of copper.

Initial Ratio of Bronze to Copper:
The initial ratio of bronze to copper is given by (4/10 * x) / (6/10 * x), which simplifies to 4/6 or 2/3.

New Ratio of Bronze to Copper:
In the new mixture, the ratio of bronze to copper is reversed, which means that the ratio becomes 3/2.

Let's assume that y parts of the mixture are drawn out and replaced with bronze. Therefore, the new quantity of the mixture is still x parts.

New Quantity of Bronze:
After drawing out y parts and replacing them with bronze, the quantity of bronze in the new mixture becomes (4/10 * x - 4/10 * y) + (y/10 * x).

New Quantity of Copper:
Similarly, the quantity of copper in the new mixture becomes (6/10 * x - 6/10 * y) + (0/10 * x).

New Ratio of Bronze to Copper:
The new ratio of bronze to copper is given by [(4/10 * x - 4/10 * y) + (y/10 * x)] / [(6/10 * x - 6/10 * y) + (0/10 * x)], which simplifies to (4/10 + y/10)/(6/10 - 6/10 * y).

Setting Up the Equation:
We want the new ratio of bronze to copper to be 3/2. Therefore, we can set up the equation (4/10 + y/10)/(6/10 - 6/10 * y) = 3/2.

Solving the Equation:
Cross-multiplying the equation, we get (4 + y)/(6 - 6y) = 3/2.

Simplifying further, we get 8 + 2y = 18 - 18y.

Rearranging the terms, we get 20y = 10.

Dividing both sides by 20, we get y = 10/20 = 1/2.

Therefore, the ratio of mixture drawn out and replaced with bronze is 1/2.

Conclusion:
The correct option is b) 1/3, which is not the same as the answer given. It seems there is a mistake in the answer provided.