5 years ago, the ratio of the age of A to that of B was 4 : 5. Five years hence, the ratio of the age of A to that of B will be 6 : 7. If, at present, C is 10 years younger than B, then what will be the ratio of the present age of A to that of C?

5 years ago, the ratio of the age of A to B = 4 : 5
Let 5 years ago, the age of A and B be 4x and 5x.
Five years hence, the ratio of the age of A to B = 6 : 7
ATQ,
$$\frac{4x + 10}{5x + 10} = \frac{6}{7}$$
28x + 70 = 30x + 60
2x = 10
x = 5
Present age of A = 4x + 5 = 4 $$\times$$ 5 + 5 = 25
Present age of B = 5x + 5 = 5 $$\times$$ 5 + 5 = 30
Present age of C = 30 - 10 = 20
Ratio of the present age of A to that of C = 25 : 20 = 5 : 4