Eighteen years ago, the ratio of A’s age to B’s age was 8 : 13. Their present ratios are 5 : 7. What is the present age of A

To solve this problem, we need to use the concept of ratios and simple algebra. Here are the steps:

Step 1: Let's denote the present age of A as 'a' and the present age of B as 'b'. According to the problem, the ratio of A's age to B's age 18 years ago was 8:13. This can be written as (a-18)/ (b-18) = 8/13.

Step 2: The problem also states that their present ages are in the ratio 5:7. This can be written as a/b = 5/7.

Step 3: Now we have a system of two equations. We can solve this system to find the values of 'a' and 'b'.

Step 4: Multiply the second equation by 18 to make the denominators of the two equations the same. We get 18a/18b = 90/126.

Step 5: Now subtract the first equation from the new second equation. We get (18a - a + 18) / (18b - b + 18) = 2/9.

Step 6: Simplify the equation to get 17a + 18 = 2b/9. Multiply both sides by 9 to get rid of the denominator on the right side. We get 153a + 162 = 2b.

Step 7: Substitute the value of 2b from the above equation into the first equation. We get (a - 18) / (153a + 162 - 18) = 8/13.

Step 8: Simplify the equation to get 13a - 234 = 8 * 135a + 8 * 144 - 144.

Step 9: Solve the equation to get a = 30.

So, the present age of A is 30 years.