Given India is UTC+5.5 and China is UTC+8, plus many other large countries are outside that range (Indonesia, Japan, Bangladesh, Mexico, Phillipines) I think you need to stretch it a bit
Given OP's 10 hour range, UTC+0 to UTC+10 is almost certainly going to be the 10 hour range that includes the most people. It includes all of Asia, Europe and Africa, and excludes both the Pacific and Atlantic oceans.
UTC+8 is all of China and UTC+5.5 is all of India, and in between are high population countries like Indonesia, Philippines, Vietnam, so UTC+5.5 to UTC+8 has to be included.
UTC+11 to UTC-8.5 is the Pacific Ocean and has maybe 10 million people total, while UTC+0 has >100 million in UK, Portugal and part of Western Africa so UTC+0 must be part of the range.
That only leaves the choice between UTC-1/2 and UTC+9/10. UTC-1 and UTC-2 have under a million with only a few small islands while UTC+10 has most of Papua New Guinea with 6 million.
