The mean of three numbers $\frac{a}{3}$, b and c is the same as the mean of the numbers $\frac{b}{3}$, $\frac{c}{3}$and x. The value of 3x is (where a, b, c are positive numbers):

a + 2b + 2c

Given  :-

\(\frac{a/3 + b + c }{3}\) = \(\frac{b/3 + c/3 + x}{3}\)

\(\frac{a}{3}\)  + b + c = \(\frac{b}{3}\)  + \(\frac{c}{3}\)  + x

a + 3b + 3c =  b + c + 3x

3x = a + 2b + 2c

So ,  a + 2b + 2c   is correct answer .