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The fraction of volume of floating body immersed in a liquid is equal to its relative density w.r.t that liquid.
Since the body floats with 1/3 volume outside water 2/3 volume is immersed inside water. So its density is (2/3)d. Where d is density of water.
As the body floats with 3/4 volume outside liquid, the volume immersed in liquid is 1/4. So its density is (1/4)d'.
d'/4 = 2d/3
= d' = 8d/3
Given density if water is 1g/cc, density if the liquid is 8/3 g/cc.
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