Let ρl be the density of liquid and ρw be the density of water.
As we know,
frequency f∝√T [where T is tension]
⇒f1f2=√T1T2...(i)
\( \begin{array}{cll}\rho \operatorname{Vg} & \rho \operatorname{Vg} & \rho \operatorname{Vg} \\ \text { fig(I) } & \text { fig(II) } & \text { fig(III) }\end{array} \)
From figure (I), (II) & (III)
T1=ρVg, [where ρ is the density of mass]
T2=ρVg−ρwVg
and T3=ρVg−ρlVg
So, putting all these values in equation (i)
we get, f1f2=√ρVgρVg−ρwVg
⇒300150=√ρρ−ρw
⇒4=ρρ−ρw⇒4ρ−4ρw=ρ
⇒ρ=43ρw .....(2)
Again,
f1f3=√T1T3=√ρVgρVg−ρlVg
⇒300100=√ρρ−ρl⇒9=ρρ−ρl
⇒9ρ−9ρl=ρ
⇒ρ=98ρl .....(3)
From equation (2) & (3),
43ρw=98ρl
⇒ρlρw=43×89=1.185≈1.18
[∵ρlρw=Relative density]