How can I purify mixed earnings from an investment fund that deals with usurious and Islamic companies and banks without knowing the exact source of the profit? And is it permissible to use these usurious earnings to pay off the interest of a usurious loan for a relative?

Certain conditions are required for the permissibility of investing in investment funds. If these conditions are not met, then investment is not permissible. The contract must be فسخ (dissolved) if possible, and the capital recovered. As for the profits held by the investor, the amount of what is unlawful therein should be determined – by tracing the fund's accounts – and spent on the welfare of Muslims (such as assisting the poor and needy, and building schools). The remainder is lawful for the investor. If dissolving the contract is not possible, then only the unlawful portion of the profits should be disbursed as mentioned. It is not permissible to give this unlawful money to a friend unless he is poor.