A 40-liter solution of 60% alcohol is mixed with ‘a’ liters of pure alcohol. If the resultant solution is 75% alcohol, find the value of ‘a’?

Sure, let's solve this step by step:

1. First, let's find out how much alcohol is there in the 40-liter solution. Since it's a 60% alcohol solution, it contains 60/100 * 40 = 24 liters of alcohol.

2. Now, let's assume that 'a' liters of pure alcohol is added to this solution. So, the total volume of the solution now becomes 40 + a liters.

3. According to the problem, this new solution is 75% alcohol. That means, the amount of alcohol in this new solution is 75/100 * (40 + a) liters.

4. But we know that the amount of alcohol in the new solution is also the sum of the alcohol in the original solution and the pure alcohol added, which is 24 + a liters.

5. Therefore, we can set up the equation 75/100 * (40 + a) = 24 + a.

6. Solving this equation will give us the value of 'a'. Let's simplify it:

   30 + 0.75a = 24 + a 0.75a - a = 24 - 30 -0.25a = -6

7. Solving for 'a' gives us a = -6 / -0.25 = 24 liters.

So, 24 liters of pure alcohol needs to be added to the 40-liter solution to get a 75% alcohol solution.