As long as the separation agreement/divorce decree states that he is responsible for the current mortgage and the 40% debt to income ratio is after you factor in your new mortgage, you should be able to qualify! Speak with a local mortgage consultant who can guide you! Depending on the new purchase price, 10K should be enough for a new property. Although, I don't recommend exhausting all of your savings, FHA requires no reserves.
Hope this helps!
Home Mortgage Consultant
Your local bank or credit union will have loan officers that can review all your financial information and then provide advice. As Realtors, we are aware of the financing needed and details of the mortgage once achieved but the mortgage lenders know all the programs available for specific cases to help home buyers. The Realtor can then help you find the home in the price point the lender and you work out. I hope you have this sorted out by now, I thought telling people where to find a mortgage lender may help someone. Good luck to you.
As Jeanne stated the best person to answer your question is a Mortgage Loan officer. Since there have been so many changes in mortgage lending they are the most informed to advise you.
Karen Paytas, GRI, CMS
Real Living Kee Realty