I wish to know what can be the best career option for my child after 10th.

Hi, both hotel management as well as travel and tourism management carry similar and very good job prospects. The choice depends on you.
For these areas, you can complete programs like post-graduate MBA and diploma programs (both full-time and distance learning). Premier institutes like Welingkar, Amity, and Indian Institute of Travel and Tourism Management offer such courses. Any person completing a graduation from a recognized institute with 50% is eligible. You will have to, of course, pass admission tests too. If possible, always choose to do a residential full-time course for better career opportunities.  
After graduation, many jobs such as front office manager, hotel administration supervisor, tour coordinator, food and beverage manager etc. shall be available.