Directions (86–90) The data below is about the staff — lab assistants and professors — in three colleges A, B and C.

Question

Directions (86–90):

The data below is about the staff — lab assistants and professors — in three colleges A, B and C.

College A: total staff (lab assistants + professors) = 82.

College B: total lab assistants = 4 more than the lab assistants in C.

College C: total lab assistants = 6 less than the professors.

Total professors in A = 44 less than the lab assistants in B.

Total staff in C = 24 more than the total staff in A.

Total professors across all three colleges = 102.

Q88. The ratio of total staff in college D to total lab assistants in A is 3 : 4, and total lab assistants in D is 20 less than that in C. Find the number of professors in D.

1. A. 24 (Correct answer)
2. B. 25
3. C. 20
4. D. 30
5. E. 50

Correct Answer

Option A — 24

Detailed Solution & Explanation

The correct answer is 24.

Key Points

• Solving the given conditions gives the staff of each college:

• Total staff in D : lab assistants in A = 3 : 4, and LA(A) = 72, so Total staff in D = (3/4) × 72 = 54.
• Lab assistants in D = LA(C) − 20 = 50 − 20 = 30.
• Professors in D = Total staff − Lab assistants = 54 − 30 = 24.