4. A solution is 40% alcohol. How much pure alcohol must be added to 200 ml of the solution to make it 50% alcohol?

Step 1: Determine the amount of alcohol in the initial solution.

The initial solution is 40% alcohol and its volume is 200 ml. So, the amount of alcohol in it is 40/100 * 200 = 80 ml.

Step 2: Let's denote the amount of pure alcohol to be added as X ml.

We want the final solution to be 50% alcohol. The final volume of the solution will be 200 ml (initial solution) + X ml (added alcohol).

So, the amount of alcohol in the final solution should be 50/100 * (200 + X) ml.

Step 3: Set up the equation and solve for X.

We know that the amount of alcohol in the final solution is the sum of the alcohol in the initial solution and the added alcohol. So, we have the equation:

80 ml (alcohol in initial solution) + X ml (added alcohol) = 50/100 * (200 + X) ml (alcohol in final solution)

Solving this equation for X gives:

80 + X = 100 + 0.5X 0.5X = 20 X = 40

So, 40 ml of pure alcohol must be added to the 200 ml solution to make it 50% alcohol.