Question

A placement company has to assign 1000 SW personnel who are skilled in Java and Dot Net to a prospective outsourcing company. He finds that 750 are having Dot Net skills and 450 have Java skills. Some have skills in both Java and Dot Net. Find the numbers who have skills in both Java and Dot Net.

• A. 250
• B. 200
• C. 350
• D. 100

Answer 1

The Correct Option is B

We need to determine how many software personnel have skills in both Java and Dot Net. Let:

• \( A \) be the set of personnel with Dot Net skills,
• \( B \) be the set of personnel with Java skills, and 
• \( |A| = 750 \)
• \( |B| = 450 \)
• \( |A \cup B| = 1000 \)

We use the formula for the union of two sets:

\(|A \cup B| = |A| + |B| - |A \cap B|\)

Substituting the known values:

\( 1000 = 750 + 450 - |A \cap B| \)

Simplifying gives:

\( 1000 = 1200 - |A \cap B| \)

\( |A \cap B| = 1200 - 1000 \)

\( |A \cap B| = 200 \)

Therefore, the number of personnel with skills in both Java and Dot Net is 200.