All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
The fact that the government or the employer has specified the distance that is covered by one liter of petrol to be ten kilometers does not make it lawful for your brother to take what is in excess of that unless he is permitted to do so by an authorized person in the place he works.
With regard to him paying some minor repairs from his own pocket, then he is not obliged to do so and he is entitled to ask his employer for what he has paid. However, this does not make it permissible for him to take the excess petrol or its price.
Allah knows best.