Final answer:
To make a 40% silver alloy, 120 liters of 20% silver must be added to the initial solution.
Step-by-step explanation:
The correct answer is option b) 30 liters.
To solve this problem, we can use the concept of the amount of silver in a solution.
We are given that the initial solution contains 80 liters of 70% silver. This means that the solution contains 0.7 * 80 = 56 liters of silver.
Let's assume that x liters of 20% silver are added to the solution. This means that x liters of the solution contain 0.2 * x liters of silver.
The final solution is required to have a silver concentration of 40%. This means that the final solution will contain (56 + 0.2 * x) liters of silver.
Now we can set up the equation:
56 + 0.2 * x = 0.4 * (80 + x)
Simplifying the equation gives:
56 + 0.2 * x = 32 + 0.4 * x
0.2 * x - 0.4 * x = 32 - 56
-0.2 * x = -24
x = -24 / -0.2 = 120
Therefore, 120 liters of 20% silver must be added to the initial solution to make a 40% silver alloy.