Explanation:

- Let's label the ages of Akhil, Sunita, and Veena as \(A\), \(S\), and \(V\) respectively.

- The average age of Akhil and Sunita is 51 years:

\((A + S) / 2 = 51\)

So, \(A + S = 102\).

- The average age of Sunita and Veena is 31 years:

\((S + V) / 2 = 31\)

So, \(S + V = 62\).

- The average age of Veena and Akhil is 33 years:

\((V + A) / 2 = 33\)

So, \(V + A = 66\).

- To find Veena's age:

- Add the three equations:

\(A + S + S + V + V + A = 102 + 62 + 66\)

\(2A + 2S + 2V = 230\)

Divide by 2:

\(A + S + V = 115\).

- Now subtract the second equation:

\(A + S + V - (S + V) = 53\)

So, \(A = 53\).

- From \(V + A = 66\), substitute \(A = 53\):

\(V + 53 = 66\)

So, \(V = 13\).

- \(\checkmark\) The correct answer is Option 1: 13 years.

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