hey deadly king i managed to work it
let say that cylinder A lost a volume V
new volume of water would be 7200(initial volume)- V
new height would be 120-(V/60)
on the other hand cylinder B has gained a volume V
new volume would be 800(initial volume)+ V
the new height would be 20+(V/40)
height difference h would be (20+(V/40))-(120-(V/60))
h=(V/24)-100
by making V subject of formula we obtain
V=24h+2400
now
as i said
dV/dt is proportional to root of h
since V= 24h+2400
d(24h+2400)/dt = -k(h)^0.5
since differential of a number is zero
24dh/dt=-k(h)^0.5
dh/dt=(-k/24)(h)^0.5
phew it was quite lengthy....