fluid doubts... from vmc modules... please help 1

for liquid having sp.gr. 1.25,

LIQUID LEVEL RISES!!

i.e. OPTION A

if the liquid was water(i.e. sp.gr.=1) then liquid level would have remained same!!

i.e option C

let an ice cube of side L is floating in the liquid!!

let sp.gr. of ice is ρ. and it floats in the liquid with a length x in the liquid!!

now, weight = upthrust( from F.B.D. )
so, L³Ïg=x.L².(1.25)g
or, xL=ρ1.25

so, xL²=ρL³1.25=volume of displaced liquid!!

now when the ice melts,

mass of ice molten = mass of water formed.
so, L³Ï=V.(1) [V=volume of water formed]

so, V=ρL³>ρL³1.25

thus water formed is more than the displaced liquid..

thus liquid level rises!!

using algebra to prove the 2nd one!!

let the ice cube with side L with sp.gr. ρ float in water.

V=vol of water displaced!!

V.1.g=upthrust=weight=L³Ïg
V=L³Ï

let x length of ice melt!!

weight of water formed=xL²Ï
vol of water formed=xL²Ï

now, wt of ice=upthrust
(L-x)L²Ïg=V_new

total volume of water displaced=V_new+water formed=(L-x)L²Ïg+xL²Ï=L³Ïg=V

so, throughout the process of melting the level of liquid remains the same!!

THUS WE CAN CANCEL OUT THE OPTION d

so ans is c