Calculating staircasing on shared ownership property

[caringissharing]

Am trying to figure this one out and cannot for the life of me work out which is the correct way round (bit thick!)
If flat is worth £100,000 and one has a 50% share and a £25,000 mortgage for ease of calculation (?!). To buy the full 100% would it be worked out:
option a) £100,000 /2 = each 50% is worth £50,000. Your share minus £25,000 mortgage leaves £25,000 equity. So to purchase it this way to buy the other £50,000 you would need to re-mortgage by £75,000?
OR
option b) Would the 50% part already be out of the question as effectively the mortgage has been cleared so that 50% is all paid for and then £25,000 equity can then be used to help with the remaining 50% so would only need re-mortgage for £25,000?
Hope this makes sense but could have big impact on whether could ever own 100% of the flat,
Thanks

To release the equity you surly need to mortgage the home? So if you own 50% and it's paid off then you need to remortgage for the other 50% which would be £50000 not £25000 and then releasing equity, but remember if the property goes up in value then you owe them more as it's the percentage you owe them not the the ££ xx

Option a. You don't own 50%. You own 25%, the bank you're mortgaged with effectively owns 25% and the HA or whoever owns the remaining 50%. The HA wants their £50k so you'd have to add this to the mortgage you already have, so you're looking for a £75k mortgage.