Hi all ,

I stumbled upon the following :

A bottle filled with water ( density 1 kilo per Litre (1000 cm3) weighs 950 grammes, filled with alcohol ( density 800 grammes ) this bottle weighs 800 grammes.

You are asked to give the volume of this bottle.

Could someone explain :

1 ) why is the solution : (950-800) / 1-0.8 ?

2) If there is a way to find the correct result by resorting to ratios ? As we know the ratio of the 2 densities per equal volume ( 1000 to 800 grammes for an equal volume of 1 decimeter^3 ) we could find values to multiply or divide the numbers of the altered ratio ( 950 to 800 ) with and thereby find the respective wheights of both the contained materials and the container.

The respective weights are 750 grammes for the water and 600 grammes for the alcohol ( the bottle weighs 200 gr).

I know we could resort to an equation but I'd like a purely arithmetical way to work that out , Euclid style.

Thanks a ton for your insight.