Let's consider two individuals, Alex and Brian. Currently, their ages are in the ratio of 56:42. In the future, Alex's age, after 24 years, compared to Brian's age 12 years ago, is in the ratio 26:12 . Determine Brian's current age.

Let's solve the problem step by step:

Step 1: Let's assign variables to the ages of Alex and Brian. Let Alex's current age be A and Brian's current age be B.

Step 2: According to the given information, their ages are in the ratio of 56:42. This can be written as A/B = 56/42.

Step 3: Simplifying the ratio, we get A/B = 4/3.

Step 4: Now, let's consider the future scenario. After 24 years, Alex's age will be A + 24 and Brian's age 12 years ago will be B - 12.

Step 5: According to the given information, the ratio of Alex's age after 24 years to Brian's age 12 years ago is 26:12. This can be written as (A + 24)/(B - 12) = 26/12.

Step 6: Simplifying the ratio, we get (A + 24)/(B - 12) = 13/6.

Step 7: Now, we have two equations: A/B = 4/3 (from Step 3) (A + 24)/(B - 12) = 13/6 (from Step 6)

Step 8: We can solve these equations simultaneously to find the values of A and B.

Step 9: Multiplying both sides of the equation A/B = 4/3 by B, we get A = (4/3)B.

Step 10: Substituting this value of A in the second equation, we get ((4/3)B + 24)/(B - 12) = 13/6.

Step 11: Cross-multiplying, we get 6((4/3)B + 24) = 13(B - 12).

Step 12: Simplifying, we get 8B + 144 = 13B - 156.

Step 13: Rearranging the equation, we get 5B = 300.

Step 14: Dividing both sides by 5, we get B = 60.

Step 15: Therefore, Brian's current age is 60.