An empty relative density bottle weighs 40g. The bottle weighs 80g when filled with methylated spirit. And 90g when filled with water. Find the...

Hello!

I think that the volumes of spirit and water were the same, and probably equal to the inner volume of a bottle. Denote this volume as

A volume a mass and a density are bounded by the relation In particular,

and

where is the density of spirit, is its mass, is the density of water and is its mass. Denote also the mass of a bottle as

The masses are actually known: and

So we have two (linear) equations and two unknowns, and From the second equation substitute it into the first equation and obtain:

We can use any units for here because is dimensionless. Therefore:

= (40/50)*1000 = 800 .