The ratio of the ages of A and B seven years ago was 3: 4 respectively. The ratio of their ages nine years from now will be 7: 8 respectively. What is B’s age at present?

Let's denote the present ages of A and B as A and B respectively.

Step 1: According to the problem, seven years ago, the ratio of A's age to B's age was 3:4. We can write this as: (A - 7) / (B - 7) = 3/4

Step 2: The problem also states that nine years from now, the ratio of their ages will be 7:8. We can write this as: (A + 9) / (B + 9) = 7/8

Now we have a system of two equations, and we can solve it to find the values of A and B.

Step 3: To solve the system, we can first cross-multiply to get rid of the fractions: 4*(A - 7) = 3*(B - 7) 8*(A + 9) = 7*(B + 9)

This simplifies to: 4A - 28 = 3B - 21 8A + 72 = 7B + 63

Step 4: We can further simplify these equations to: 4A - 3B = 7 8A - 7B = -9

Step 5: Now we can solve this system of equations using any method we like (substitution, elimination, etc.). If we multiply the first equation by 2 and subtract the second equation from the result, we get: 2*(4A - 3B) - (8A - 7B) = 2*7 - (-9) 8A - 6B - 8A + 7B = 14 + 9 B = 23

So, B's present age is 23 years.