What is the greatest problem of the present day world?

I think that you mean to ask, "What is the greatest problem of the present-day world?" The answer to this question is a matter of personal opinion, but one that should be based on the issues that are most frequently discussed with concern. People, depending on their nationality, level of education, and other factors, will have varying opinions about the level of importance of the things that impact us the most.
Globally, most people are concerned with the environment, particularly the long-term effects of climate change. This is a global concern because the effects of the warming of the Earth will impact everyone, albeit in different ways. The accelerated melting of ice caps in the Arctic causes rising sea levels, which leads to flooding in low-lying areas. Also, very hot parts of the world, such as the Middle East, North Africa, and Sub-Saharan Africa, will get hotter. When conditions in these regions make them uninhabitable for humans, natives will have to move to northern climes. Once again, we will probably see a backlash against refugees, as well as concerns about overcrowding and the dilution of national culture by foreign influence. Climate change can also lead to food shortages.
Concerns about starvation also exist. In the United States, we talk frequently about "food deserts," communities that lack access to stores with fresh fruits and vegetables and whole grains.
Other global concerns include the rights of minorities and the equal treatment of women and girls. The current "ethnic cleansing" of the Rohingya Muslim minority in Burma is an example of how the rights of minorities are still elusive.