A mixture of acid and water of 25 litres contain 20% acid. What quantity of water should be added to make the level of acid to 10%?
To solve this problem, we need to find the amount of acid and water in the initial mixture and then determine the amount of water needed to adjust the concentration.
Step 1: Find the amount of acid in the initial mixture.
If the mixture is 25 liters and contains 20% acid, we can calculate the amount of acid as follows:
Acid in liters = 25 liters x 20% = 25 liters x 0.2 = 5 liters
Step 2: Determine the amount of water in the initial mixture.
Since the total volume of the mixture is 25 liters and we know there are 5 liters of acid, we can find the amount of water as follows:
Water in liters = Total volume - Acid volume = 25 liters - 5 liters = 20 liters
Step 3: Calculate the amount of water needed to adjust the concentration.
We want to end up with a mixture of 10% acid. Let's assume we need to add "x" liters of water to achieve this.
The new volume of water in the mixture will be (20 liters + x liters). The sum of acid and water should equal the total volume of the mixture, which is 25 liters. Therefore, we can create the following equation:
Acid in liters + Water in liters = Total volume
5 liters + (20 liters + x liters) = 25 liters
Simplifying the equation:
25 liters + x liters = 25 liters
x liters = 25 liters - 20 liters
x liters = 5 liters
Therefore, you need to add 5 liters of water to the mixture to make the level of acid 10%.
To solve this problem, we need to determine the quantity of water that should be added to the mixture in order to achieve a 10% level of acid. Here's how we can approach the question:
Step 1: Calculate the amount of acid in the initial mixture
Given that the initial mixture contains 20% acid, we can deduce that it contains 20% of 25 liters:
Acid in the initial mixture = 20/100 * 25 = 5 liters.
Step 2: Calculate the desired amount of acid in the final mixture
To obtain the desired 10% level of acid in the mixture, we need to find the total quantity of the final mixture (which includes both water and acid).
Let's assume the amount of water that needs to be added is 'x' liters.
Therefore, the total volume of the final mixture would be (25 + x) liters.
According to the question, the final mixture should contain 10% acid, which is 10% of (25 + x) liters:
Desired acid in the final mixture = 10/100 * (25 + x) = (2.5 + 0.1x) liters.
Step 3: Equate the amounts of acid in the initial mixture and the final mixture
Since we're only adding water to the mixture to dilute the acid without removing any acid, the quantity of acid in the initial mixture should be equal to the quantity of acid in the final mixture.
Therefore, we can set up the equation:
Acid in the initial mixture = Desired acid in the final mixture.
5 = 2.5 + 0.1x
Step 4: Solve for x
Simplifying the equation:
0.1x = 5 - 2.5
0.1x = 2.5
Dividing both sides by 0.1:
x = 25
So, the quantity of water that should be added to the mixture is 25 liters in order to achieve a 10% level of acid.
To summarize:
To make the level of acid 10% in a mixture of 25 liters containing 20% acid, you need to add 25 liters of water.
let the amount of water to be added be x L
looking at the amount of acid we have:
.20(25) + 0(x) = .10(25 + x)
solve for x