Question

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. 250
• B. 200
• C. 350
• D. 100

Hint:

Use n(A union B) = n(A) + n(B) - n(A intersect B), with the union equal to the total group.

Answer 1

The Correct Option is B

Step 1: Identify what is known.
Total software personnel to be assigned = 1000. Number skilled in .Net = 750. Number skilled in Java = 450. Some professionals have both skills, and we need to find how many.
Step 2: Recognize this as a set theory union problem.
Since every one of the 1000 personnel is being assigned based on having at least one of these two skills, the union of the two skill groups covers the entire group of 1000 people. If D is the set with .Net skills and J is the set with Java skills, then n(D union J) = 1000.
Step 3: Apply the union formula.
The formula for the union of two overlapping sets is: n(D union J) = n(D) + n(J) - n(D intersect J), where n(D intersect J) is the number with both skills, which is what we want.
Step 4: Substitute the known values.
1000 = 750 + 450 - n(D intersect J)
1000 = 1200 - n(D intersect J)
n(D intersect J) = 1200 - 1000 = 200
Step 5: Verify and match with options.
If 200 people have both skills, then people with only .Net = 750 - 200 = 550, and people with only Java = 450 - 200 = 250. Adding these three exclusive groups: 550 + 250 + 200 = 1000, which matches the total. This confirms the answer is 200, option (2).