Capital gains tax on amount received from Sale of Flat

Since mother is owner, the tax liability on capital gains will arise to her on the entire consideration received (even though 75% of it will go to you), she needs to plan her taxes and as far as your case is concerned the 75% share will be gift from your mother and will not attract any type of taxes. You can invest any amount of the gift received to acquire the property. 

Further from the details given by you, the sale consideration would be approximately Rs.33,33,333/-. The Indexed cost of acquisition is Rs.620,058/-. The capital gain arising on the sale is Rs.27,13,275 (Since CII of FY 2011-12 is not yet announced the CII of 2010-11 is taken as base). Your mother has to utilize this amount of capital gains in purchasing another house or alternately investing in REC/NHAI bonds. In case she does not do both and instead chooses to gift 75% of the amount of sale consideration straight away to you then in such case she has to bear tax on LTCG to a tune of Rs.558,930/-.