Average age of A and B is 30 years, that of B and C is 32 years and the average age of C and A is 34 years.The age of C is3334 years35 years36 years

Given that the average age of A and B is 30 years, we can write this as:

(A + B)/2 = 30 => A + B = 60 ----(1)

Similarly, given that the average age of B and C is 32 years, we can write this as:

(B + C)/2 = 32 => B + C = 64 ----(2)

And given that the average age of C and A is 34 years, we can write this as:

(C + A)/2 = 34 => C + A = 68 ----(3)

Now, if we add equations (1) and (2), we get:

A + B + B + C = 60 + 64 => A + 2B + C = 124 ----(4)

And if we subtract equation (3) from equation (4), we get:

A + 2B + C - (C + A) = 124 - 68 => B = 56

Substituting B = 56 in equation (2), we get:

56 + C = 64 => C = 64 - 56 => C = 8

So, the age of C is 8 years.

Given that the average age of A and B is 30 years, we can write this as:

(A + B) / 2 = 30 => A + B = 60 ----(1)

Similarly, given that the average age of B and C is 32 years, we can write this as:

(B + C) / 2 = 32 => B + C = 64 ----(2)

And given that the average age of C and A is 34 years, we can write this as:

(C + A) / 2 = 34 => C + A = 68 ----(3)

Now, adding equations (1), (2) and (3), we get:

2(A + B + C) = 60 + 64 + 68 => 2(A + B + C) = 192 => A + B + C = 96 ----(4)

Subtracting equation (1) from equation (4), we get:

C = 96 - 60 => C = 36

So, the age of C is 36 years.

Let's solve this step by step:

1. The average age of A and B is 30 years, which means the sum of their ages is 2*30 = 60 years.
2. The average age of B and C is 32 years, which means the sum of their ages is 2*32 = 64 years.
3. The average age of C and A is 34 years, which means the sum of their ages is 2*34 = 68 years.

Now, if we add the first two equations, we get: A + B + B + C = 60 + 64 2B + A + C = 124 ----(i)

And if we subtract the third equation from this, we get: 2B + A + C - (A + C) = 124 - 68 2B = 56

So, B = 56 / 2 = 28 years.

Substitute B = 28 years in the second equation (B and C's average age): 28 + C = 64 So, C = 64 - 28 = 36 years.

So, the age of C is 36 years.