Is it permissible for me to take 40% of the partnership's profit, after introducing another partner with an additional sum, without his knowledge of my percentage?

It is not permissible to give one's money to another for investment (mudarabah) without their permission. If permission is granted, the one who gives the money is not entitled to any of the profits because he is an agent. It is permissible to agree upon a known fee for the agency. However, if the one who gives the money stipulates a share of the profit, the contract becomes void, and the investment agent (mudarib) is entitled to a customary wage (ajr al-mithl), with all profits belonging to the owner of the capital.