A salt solution of 15 litres contains 20%salt. How much water must you add to salt solution, in order to dilute it 15% salt?
3 litres
you are diluting it 20/15=1.333 time, which means one part of the original (1 part = 15 liters) and .333 parts water (.333*15)=5 liters water.
To solve this problem, you need to calculate the amount of salt present in the initial solution and then calculate how much water you need to add to achieve the desired concentration.
Step 1: Calculate the amount of salt in the initial solution.
The initial solution contains 20% salt. This means that for every 100 parts of the solution, 20 parts are salt. Therefore, the amount of salt in the solution can be calculated as:
(20/100) * 15 litres = 3 litres of salt
Step 2: Calculate the total volume of the solution after dilution.
To achieve a 15% salt concentration, the total volume of the solution after dilution will be the sum of the initial solution volume and the volume of water added. Let's denote the volume of water added as 'x'. Therefore, the total volume of the solution after dilution can be expressed as:
15 litres + x litres
Step 3: Calculate the amount of salt in the diluted solution.
The diluted solution is desired to have a 15% salt concentration. This means that for every 100 parts of the solution, 15 parts are salt. Therefore, the amount of salt in the diluted solution can be calculated as:
(15/100) * (15 + x) litres
Step 4: Set up the equation and solve for 'x'.
Now we can set up an equation based on the two amounts of salt calculated in steps 1 and 3:
3 litres = (15/100) * (15 + x) litres
To solve this equation, we can first eliminate the fraction by multiplying both sides of the equation by 100:
300 = 15 * (15 + x)
Expand the equation:
300 = 225 + 15x
Rearrange the equation:
15x = 300 - 225
15x = 75
Divide both sides of the equation by 15:
x = 75/15
x = 5
Therefore, you need to add 5 litres of water to the salt solution in order to dilute it to a 15% salt concentration.