How to Calculate Fees If There Is No Agreement
Question

I have a question about selling and hiring. There is a young man who offers tutoring services in return for a set fee per hour. A relative of his asked him to tutor his son, but the father did not ask the tutor about the fee, because he trusts him, and he gave him a sum of money in advance. The young man already had a figure per hour in mind. Then he started to keep a record of the hours, until the payment in advance had been used up. Now the father owes him money. But the tutor has not told him how much he owes him. Then he realised that the fee that he had in mind was very low, no more than 60% of the minimum going rate for this service. 
The question is: Can he increase his fee to 75-80% of the going rate, without informing the father? If that is permissible, can he charge this rate for future hours but not for the past hours, or for both?
Praise be to Allah.Calculating tutoring fees 
If there was agreement on the work to be done but no mention of the fee, and this young man is known to tutor in return for payment – as appears to be the case – then the hiring contract is valid, and he is entitled to the going rate. It does not matter what the young man intended to charge.
It says in ar-Rawd al-Murbi‘ (p. 410): 
“If a person enters a public bath or embarks on a ship without an agreement on a fee, or he gives his cloth to a dyer or tailor to work on it, without an agreement on a fee, that is valid, on the basis of the usual going rate, because what is known to be the going rate is as good as stating the rate. The same applies if he gives his goods to someone to sell them, or he employs a porter to carry them, and the like. The worker is entitled to the going rate, even if he does not usually charge a fee.”
If he wants to give up some of his dues and take less than that, as a favour to the father of the student, there is nothing wrong with that. As for increasing it above what tutors usually charge in his city, that is not permissible without the express agreement of the father of the student.
Combining hiring and giving a loan: Valid?
It is not valid to combine hiring and giving a loan , because the Prophet (blessings and peace of Allah be upon him) said: “It is not permissible to arrange a loan combined with a sale.” Narrated by at-Tirmidhi (1234), Abu Dawud (3504), an-Nasa'i (4611); classed as sahih by at-Tirmidhi and al-Albani.
Hiring means selling benefits. The majority of scholars are of the view that it is not allowed to combine a loan with any kind of exchange transaction, such as brokerage , for example.
If what is meant is that the father gave him payment in advance, there is nothing wrong with that, if the fee is known. But if it is unknown and the contract is invalid, then what he has in hand is like a trust, but if he uses it, it becomes like a loan.
And Allah knows best.