If d is the density of a solution of a solute(molar mass = W) in a solvent and m is the molality , then prove that molarity(M) of this solution is
M = (1000d m)/(1000 + mW)

let weight of the solvent be w gm and weight of the solution be Wgm
then weight of the solvent=(W-w)gm

density D=W/V (V=volume of the solution)

molality m=(w x1000)/(M'x(W-w))

this implies, (W-w)=(w x1000)/(M'xm)

=> W=w [(1000+M'm)/M'm]

now,
molarity M=(w x1000)/(M' x V)

=> V=(w x1000)/(MxM')

now
D=W/V
=> D=[{(1000+M'm)/M'm}/{1000/MM'}]

=> D=[(1000+M'm)xMM'] / [1000x M'm]