There are three positive numbers. One third of average of all three numbers is 8 less than value of highest number. The average of lowest and second lowest number is 8. What is highest number?

Let the three positive numbers in increasing order be a, b and c and the average of these numbers be be A.
Then,
$$\frac{{a + b + c}}{3} = A.....(i)$$
Given,
$$\eqalign{ & c - \frac{A}{3} = 8 \cr & \Rightarrow c - \frac{{a + b + c}}{9} = 8.....(ii) \cr} $$
Also given,
$$\eqalign{ & \frac{{b + a}}{2} = 8 \cr & \Rightarrow a + b = 16.....(iii) \cr} $$
Putting the value of (a + b) in equation (ii), we get
$$\eqalign{ & \Rightarrow c - \left( {\frac{{16 + c}}{9}} \right) = 8 \cr & \Rightarrow 9c - 16 - c = 72 \cr & \Rightarrow 8c = 72 + 16 \cr & \Rightarrow 8c = 88 \cr & \Rightarrow c = 11 \cr} $$
? Highest number = 11