Methyl group will increase the hydrophobicity. Usually organic aromatic and aliphatic compounds are insoluble in water and increase hydrophobicity. Functional groups (electron donating or withdrawing)  that can form hydrogen bond with water can affect the hydrophobic behavior (like dissolve like). 

Dear Prasad G. Mahajan ,

Addition of alkyl group will again increase hydrophobicity, because of this you solubility difference will be there.

Addition of methyl group by removing H, it again increase hydrophobicity, so solubility in acidic solvents remains constant but in aqueous solvents decreases.

addition of methyl group will increase stability of your compound. the sensitive reactivity will be decreases.

As same water solubility not at all possible.

Good Luck & Regards

R.Selva............. 

Because it is a long story to explain how to predict the effects of a group (lipophilicity, steric, and electronic parameters)

Please read the following and try to read the references cited theirin

http://en.wikipedia.org/wiki/Partition_coefficient

Best to look up the Partition Coefficient of any substituent group that you are interested in. This allows one to calculate whether the addition of such a group to a molecule will increase or decrease the lipophilicity of the substance. Many books on drug design contain tables of these numbers. One such book, although old by now, is  "Selective Toxicity" by Adrien Albert.

Thank you everyone for your valuable guidance 

Alkylation increases hydrophobicity

the effects of substituents (group) on hydrophobic characters of organic compounds which are decreased. This is because of hydrogen bonding and dipolar interaction hydrophilic characters are increased.