A wooden block floating in a bucket of water has 45 of its volume submerged. When a certain amount of oil is poured into the bucket, it is found that the block is just under the oil surface with half of its volume under water and half in oil. The density of oil relative to that of water is?

Correct option is C. 0.6
In 1st situation
Vbρbg = Vsρw
Vs/Vb = ρb/ρw = 4/5.. (i)
here Vb is volume of block
Vs is submerged volume of block
ρb is density of block
ρw is density of water
Let ρo is the density of oil
Finally in equilibrium condition
Vbρbg = (Vb/2)ρog + (Vb/2)ρwg
ρb = (ρo + ρw)/2
⇒ ρo/ρw = 2ρb/ρw - 1 = 2(4/5) - 1 = 3/5 = 0.6