To determine the amount of the 5% solution (let's call it \(x\) liters) and the amount of the 40% solution (which will be \(10 - x\) liters, since the total volume must be 10 liters), we can set up an equation based on the total amount of acid in the final mixture.
The target is to create 10 liters of a 20% solution, which means the total amount of acid needed is: \[ 0.20 \times 10 = 2 \text{ liters of acid} \]
The amount of acid contributed by the 5% solution is: \[ 0.05x \text{ liters of acid} \]
The amount of acid contributed by the 40% solution is: \[ 0.40(10 - x) \text{ liters of acid} \]
To find the correct equation, we set the total amount of acid equal to the amount needed (2 liters): \[ 0.05x + 0.40(10 - x) = 2 \]
This matches option B: \[ (0.20)(10) = 0.05x + 0.40(10 - x) \]
Thus, the correct answer is B.