How many kilograms of water must be evaporated from 10kg of an 8% salt solution to produce a 25% salt solution

To find out how many kilograms of water must be evaporated, we need to understand the concept of concentration and the process of evaporation.

Let's break down the problem step by step:

1. Start with the initial solution: We have 10 kilograms of an 8% salt solution. This means that in 10 kilograms of solution, 8% (or 0.08) of it is salt.

2. Determine the amount of salt in the initial solution: To find the amount of salt in the initial solution, we multiply the total weight of the solution (10 kilograms) by the concentration of salt (0.08):
Salt in initial solution = 10 kg * 0.08 = 0.8 kg

3. Set up the equation: Let's assume that 'x' kilograms of water must be evaporated to obtain a 25% salt solution.

4. Calculate the amount of salt after evaporation: The amount of salt after evaporation will remain the same, but the total amount of solution will decrease. If 'x' kilograms of water are evaporated, the total amount of solution will be reduced to (10 - x) kilograms. So, the amount of salt after evaporation is:
Salt after evaporation = 0.8 kg

5. Determine the concentration after evaporation: The concentration of the salt solution after evaporation is 25% or 0.25. This means that in the reduced amount of solution (10 - x) kilograms, 25% (or 0.25) of it is salt. Therefore, the amount of salt after evaporation is:
Salt after evaporation = 0.25 * (10 - x)

6. Set up the equation: Since the amount of salt after evaporation is the same as the initial solution, we can equate the two amounts:
0.25 * (10 - x) = 0.8

7. Solve for 'x': Now, we can solve the equation to find 'x', which is the amount of water that needs to be evaporated.
2.5 - 0.25x = 0.8
0.25x = 2.5 - 0.8
0.25x = 1.7
x = (1.7 / 0.25) ≈ 6.8

Therefore, approximately 6.8 kilograms of water must be evaporated from the initial 10-kilogram solution to obtain a 25% salt solution.