Answer
$q_A = \frac{3Q}{8}$
$q_B = \frac{Q}{4}$
$q_C = \frac{3Q}{8}$
Work Step by Step
Since the spheres are identical, when two spheres are brought in contact, the charges will arrange themselves so that both spheres have the same net charge.
Initially:
$q_A = Q$
$q_B = 0$
$q_C = 0$
After sphere A touches sphere B:
$q_A = \frac{Q}{2}$
$q_B = \frac{Q}{2}$
$q_C = 0$
After sphere B touches sphere C:
$q_A = \frac{Q}{2}$
$q_B = \frac{Q}{4}$
$q_C = \frac{Q}{4}$
After sphere C touches sphere A:
$q_A = \frac{3Q}{8}$
$q_B = \frac{Q}{4}$
$q_C = \frac{3Q}{8}$
