Let us assume that A goes down with an acceleration a1 and block B down with an acceleration a2. Let us say the block C moves with an acceleration a3 upwards. The equations of motion for them are:

3 g - T = 3 a1 => T = 3 g - 3 a1 --- eq 1

5 g - T = 5 a2 => T = 5 g - 5 a2 -- eq 2

2 T - 6 g = 6 a3 => 2 T = 6 g + 3 (a1+a2) -- eq 3

a3 = (a1+a3)/2 as block C moves up (x1+x2)/2 distance when A moves down by x1 and B moves down by X2 distance.

Solving the above three equations, eq 1 + eq 2 = eq 3

2T = 3 g - 3 a1 + 5 g - 5 a2 = 6 g + 3 a1 + 3 a2 => 2 g = 6 a1 + 8 a2

3 a1 + 4 a2 = g -- eq 4

eq1 = eq 2 => 3 g - 3 a1 = 5 g - 5 a2 => 5a2 - 3a1 = 2g -- eq 5

add eq 4 and eq 5 => 9 a2 = 3 g => a2 = g/3

a1 = [ g - 4 g / 3 ] /3 = -g/9

a3 = (a1+a2)/2 = g/9 T = 3g - 3a1 = 10g/3

*Block A upwards with g/9 , B downwards with g/3, C upwards with g/9*

*Tension all along the string is same = 10 g/3*