What is the value used to calculate the new partner's share in a taxi: is it the estimated value of the car before repairs, or is the value of the repairs that increased its price added to it?

For a partnership to be valid, the capital must be present and in cash at the time of the contract. The Malikis and Hanbalis permitted the validity of a partnership using ‘urūd (goods, such as a car), provided they are appraised and their value is determined as capital at the time of the contract. Therefore, for your partnership involving the car, it must be appraised before the contract, and its value considered as your capital. The amount paid by the third partner for repairs will then be considered their capital.