3 metal plates a,b,c.distance between a-b is 2d and distance between b-c is d.A and b are connected to ground via switch s1,s2.there is charge q on b. find the charge thatt flows throuugh s1,s2 when both switches are closed.

Considering all 3 metal plates a,b,c having same area of cross section.Hence capacitance btw. 'a' & 'b' be C(say),then btw. 'b' & 'c' will be 2C.

Now 'b' must've same potential(say V) all over it's surface.So let Q be the induced negative charge on 'a' then q-Q wiil be on 'c'.

or,  CV=Q & 2CV=q-Q.Solving them will give Q=q/3.

So when switches s1 & s2  are closed then total charge flowed=q(through s2)-q/3(through s1)=2q/3