Question

IP A block of wood floats on water. A layer of oil is now poured on top of the water to a depth that more than covers the block, as shown in the figure

If 91{\rm {\rm \\%}} of the wood is submerged in water before the oil is added, find the fraction submerged when oil with a density of 880kg/m3 covers the block.

Answer 1

If 91% of the wood is submerged in the water before the oil is poured, and the mass of the block is M, and the volume of the block is V, and

The density of water is 1000 kg/m^3
The density of air is 1.225 kg/m^3 (from Wikipedia)

M = 1000 * V * 0.91 + 1.225 * V * (1 - 0.91)

When the oil is added the new fraction (P) of the block submerged in water is given by

M = 1000 * V * P + 821 * V * (1 - P)

So
1000 * 0.91 + 1.225 * 0.09 = 1000 * P + 821 - 821 * P
910 + 0.11025 = 179 * P + 821
P = 89.11025 / 179 = 0.4978
or
49.78% of the block will be below the water line (submerged in water), the rest will be above the water and will be in the oil layer.