A container has 20 liters of a solution containing alcohol and water in the ratio of 3:2. How many liters of water should be added to make the ratio 3:4? Options 10 6 4 8
Question
A container has 20 liters of a solution containing alcohol and water in the ratio of 3:2. How many liters of water should be added to make the ratio 3:4? Options
10
6
4
8
Solution
The initial volume of the solution is 20 liters, and the ratio of alcohol to water is 3:2. This means that the solution contains 12 liters of alcohol and 8 liters of water.
We want to add water to change the ratio to 3:4, but the amount of alcohol will remain the same (12 liters).
Let's denote the amount of water to be added as x. The new total volume of the solution will be 20 + x liters.
According to the problem, the ratio of alcohol to water in the new solution should be 3:4. This means that the amount of alcohol (12 liters) should be 3/7 of the total volume of the solution (because 3 is 3 out of 7 parts in the ratio 3:4).
So, we can set up the equation: 12 = 3/7 * (20 + x)
Solving this equation for x gives us: x = 28 - 20 = 8 liters.
So, 8 liters of water should be added to the solution to make the ratio of alcohol to water 3:4.
Therefore, the correct answer is 8.
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