Consider the situation shown in figure. Both the pulleys and the string are light and all the surfaces are frictionless. Find the tension in the string.

Clearly from the figure,

for block of mass "M"

$Mg-T=Ma$ ...........(i)

from block of mass "2M"

$2T=2M\left(\frac{a}{2}\right)$ ........(ii)

sustitue value of $a$ from equation (i), we get

$2T=2M\left(\frac{Mg-T}{2M}\right)$

$2T=Mg-T$

hence,

$T=\frac{Mg}{3}$