1. **State the problem:** We need to find the number of participants who are university graduates from Ekiti state working in the banking sector. 2. **Given data:** - Total participants: 290 - From Ekiti state: 120 - University graduates: 110 - From banking sector: 130 - University graduates working in banking sector: 55 - Bankers from Ekiti state: 60 - University graduates from Ekiti state: 70 - Participants from other states who are HND holders working in manufacturing: 75 3. **Define variables:** Let $x$ be the number of university graduates from Ekiti state working in the banking sector (what we want to find). 4. **Use the principle of inclusion-exclusion and given intersections:** - University graduates working in banking sector = 55 - Bankers from Ekiti state = 60 - University graduates from Ekiti state = 70 5. **Note:** The number $x$ must be less than or equal to each of these intersecting groups. 6. **Use the formula for intersection of three sets:** $$|U \cap E \cap B| = |U \cap B| + |E \cap B| + |U \cap E| - |U| - |E| - |B| + |Total|$$ But since we don't have all intersections, we use the fact that: $$x \leq |U \cap B| = 55$$ $$x \leq |E \cap B| = 60$$ $$x \leq |U \cap E| = 70$$ 7. **Calculate participants from other states:** Participants from other states = Total - Ekiti state = 290 - 120 = 170 8. **Given 75 participants from other states are HND holders working in manufacturing, so the rest from other states are not university graduates or bankers in Ekiti. This does not affect $x$ directly.** 9. **Since $x$ is the number of university graduates from Ekiti state working in banking sector, and the minimum of the three intersecting pairs is 55, the maximum possible $x$ is 55.** 10. **Therefore, the number of university graduates from Ekiti state working in banking sector is:** $$\boxed{55}$$