A constant immersion hydrometer floats vertically in water when the weight of its float is 30 g. When it is made to float in the liquid ( miscible in water ), the weight of its float is increased by 10 g. Find the weight of the hydrometer when its is floated in a mixture containing equal masses of water and the liquid.

Suppose m is the real mass of the hydrometer and volume is v. Now supposemw  is the mass of water displace and ml is the mass of other liquid displaced.So we havem-mw=30 g............................(1)m-ml=30+10=40 g.............(2)Now when hydrometer is immeresed in mixure then water displaced will be mw2 and liquid displaced will be ml2. So the weight of the hydrometer will be m- mw2-ml2.Now adding equation (1) and (2) we have2m-mw-ml=70deviding by 2 we getm- mw2-ml2=35. So the weight of the hydrometer will be 35 g. 

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