The product of the ages of A and B is 240. If twice the age of B is more than A’s age by 4 years, what was B’s age 2 years ago?

Let's denote A's age as a and B's age as b.

From the problem, we know that:

1. a * b = 240 (The product of the ages of A and B is 240)

2. 2b = a + 4 (Twice the age of B is more than A’s age by 4 years)

We can solve these equations step by step:

Step 1: From equation 2), we can express a in terms of b: a = 2b - 4

Step 2: Substitute a in equation 1): (2b - 4) * b = 240

Step 3: Simplify the equation: 2b^2 - 4b - 240 = 0

Step 4: Divide the equation by 2 to simplify: b^2 - 2b - 120 = 0

Step 5: Factor the equation: (b - 12)(b + 10) = 0

Step 6: Solve for b: b = 12 or b = -10. Since age cannot be negative, b = 12.

So, B's age is 12.

To find B's age 2 years ago, subtract 2 from 12: 12 - 2 = 10.

Therefore, B's age 2 years ago was 10 years.