Question:easy
A placement company has to assign 1000 software professionals skilled in Java and .Net to a prospective outsourcing company. It finds that 750 have .Net skills and 450 have Java skills, with some professionals skilled in both. Find the number of professionals who have skills in both Java and .Net.
A placement company has to assign 1000 software professionals skilled in Java and .Net to a prospective outsourcing company. It finds that 750 have .Net skills and 450 have Java skills, with some professionals skilled in both. Find the number of professionals who have skills in both Java and .Net.
Show Hint
Use n(A union B) = n(A) + n(B) - n(A intersect B), with the union equal to the total group.
Updated On: Jul 15, 2026
- 250
- 200
- 350
- 100
Show Solution
The Correct Option is B
Solution and Explanation
We can also solve this by directly building the Venn diagram regions instead of jumping to the union formula.
- Picture two overlapping circles: one for .Net skills (750 people) and one for Java skills (450 people), placed inside a rectangle representing the full group of 1000 people.
- Let the overlapping region, people with both skills, have b people. Then the .Net-only region has (750 - b) people, and the Java-only region has (450 - b) people.
- Since every one of the 1000 people falls into one of these three non-overlapping regions, their sum must equal 1000: (750 - b) + (450 - b) + b = 1000.
- Simplify the left side: 750 + 450 - b - b + b = 1000, which becomes 1200 - b = 1000.
- Solving for b: b = 1200 - 1000 = 200.
- Check: .Net-only = 750 - 200 = 550, Java-only = 450 - 200 = 250, both = 200. Total = 550 + 250 + 200 = 1000, which matches, confirming the overlap is correct.
So 200 professionals have skills in both Java and .Net, matching option (2). \[\boxed{200}\]
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