Is there concession(for prayer and fasting) for someone who travel for both bad and good things but his main aim is the good thing ?.

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.

If by 'bad things' you mean sins, then most jurists hold the view that the traveler whose travel is for committing a sin, does not benefit of the concessions of travel, such as shortening and combining the prayers, and breaking the fast in Ramadhaan. This is if his travel is purely to commit a sin.

However, if by his travel, he wants to achieve both a permissible matter and a forbidden one, then we have to look at whether the two matters are equal, meaning the permissible matter and the forbidden one. If his intention for what is forbidden is predominant, then it is not permissible for him to benefit from the concessions of travel. However, if he predominantly intends a permissible matter, then it is permissible for him to benefit from the concessions of travel.

Ibn Al-Muflih, from the Hanbali School of jurisprudence, said in Al-Insaaf:

"If his intention by travel is most for a permissible matter, then it is permissible for him to shorten the prayer according to the correct view of the School [..] Another view is that it is not permissible. Nonetheless, if his intentions for what is permissible and what is forbidden are equal, or that he predominantly intends to do what is forbidden, then he is not permitted to shorten the prayer, and this is the view of all the Hanbali scholars." [End of quote]

For more benefit on traveling in order to avoid fast in Ramadan, please refer to the following article: 187975

Allah knows best.