Well to be honest there are emny problems that bitcoins can solve. Here is the list of the ones that I find most influential:-
3.Its keeping check on the whales and the big business personalities who are in association with banks controlling the people and their money, not always it is beneficial for them, most of the times it's biased .
These are no the only problems in the world. Bitcoin can solve some basic human problems such as enabling the poor an equal opportunity to start from nothing and earn a living. But human nature is such that some have the intrinsic urge to be successful more than others. These and many more also contribute to the world having endless problems.