The ratio of ages of A and B is 4:5 and that of B and C is 3:2. Find the age of B after 10 years. Statement I: Difference between the ages of C and A after 10 years and the difference between ages of A and B after 10 years is same. Statement II: Difference between ages of A and C is 4 years.

We are given: The ratio of ages of A and B 4:5. The ratio of ages of B and C is 3:2. We are tasked with finding B's age after 10 years. Let:

A's age = 4x B's age = 5x, C's age = 10x/3.

Statement I The difference between the ages of C and A after 10 years is the same as the difference between the ages of A and B after 10 years. This implies: (C+10)−(A+10)=(B+10)−(A+10). C−A=B−A. Substituting the values in terms of x:

Solving for x determines A,B, and C's ages. Statement I is sufficient.

The difference between C and A is 4 years: C − A = 4. Substituting values: Simplify:

Solving for x determines A,B, and C's ages. Statement II is sufficient.

Either Statement I or II alone is sufficient.