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When a cube is floating in water, 20% of the cube is outside the water. When the same cube is placed in another liquid, 35% of the cube is outside the liquid. The density of the liquid in gcm^-3 is

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$\frac{16}{13}$

$\frac{4}{13}$

$\frac{13}{20}$

$\frac{4}{5}$

answer is A.

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Detailed Solution

For the cube in water

$ρ_{s} Vg = ρ_{w} (0.8 V) g$

For the cube in liquid

$ρ_{s} Vg = ρ_{l} (0.65 V) g$

$\Rightarrow ρ_{l} = \frac{0.8}{0.65} ρ_{w} = \frac{16}{13} ρ_{w}$

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