Two blocks A and B of masses 3m and m, respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in figure. The magnitudes of acceleration of A and B immediately after the string is cut, are respectively

Initially system, is in equilibrium with a total weight of 4mg over spring
When string is cut at the location as shown
So, force on mass, B = mg
$\therefore$ Acceleration of mass, B = g
For mass A ; free body diagram is 
If a = acceleration of block of mass A, then
${\text{F}}_{\text{net}}=4\text{\hspace{0.17em}mg}-3\text{\hspace{0.17em}mg}$
$\Rightarrow 3{\text{\hspace{0.17em}m\hspace{0.17em}.\hspace{0.17em}a}}_{\text{A}}=\text{mg}$ or ${\text{a}}_{\text{A}}\text{=}\frac{\text{g}}{\text{3}}$
So, accelerations for blocks A and B are
${\text{a}}_{\text{A}}=\frac{\text{g}}{\text{3}}$ and ${\text{a}}_{\text{B}}=\text{g}$