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 ages of A and B as A and B respectively. According to the problem, the ratio of their ages 18 years ago was 8:13. This means that (A-18)/8 = (B-18)/13.

Step 2: We also know that their present ages are in the ratio 5:7. This means that A/5 = B/7.

Step 3: Now we have a system of two equations, and we can solve it. Let's express B from the second equation: B = 7A/5.

Step 4: Now we can substitute B in the first equation: (A-18)/8 = (7A/5 - 18)/13.

Step 5: To simplify the calculations, let's multiply all terms by 40 (which is the least common multiple of 8, 5, and 13): 5A - 90 = 56A/13 - 90.

Step 6: Let's get rid of the fractions by multiplying all terms by 13: 65A - 1170 = 56A - 1170.

Step 7: Now we can solve this equation for A: 65A - 56A = 1170, so 9A = 1170, and A = 130.

So, the present age of A is 130 years.