Read the information and answer the question given below. The information is…

2025

Read the information and answer the question given below. The information is about the staff (lab assistants and professors) in colleges A, B, C and D.

  • In A, the total of lab assistants and professors is 82.

  • In B, the total lab assistants are 4 more than the total lab assistants in C.

  • In C, the total lab assistants are 6 less than the total professors.

  • The total professors in A are 44 less than the total lab assistants in B.

  • The total staff in C are 24 more than that in A, and the total professors in all the colleges are 102.

  • The ratio of total staff in college D to lab assistants in A is 3 : 4.

  • The total lab assistants in D are 20 less than that in C.

Find the number of professors in D.

  1. A.

    24

  2. B.

    25

  3. C.

    20

  4. D.

    30

  5. E.

    50

Show answer & explanation

Correct answer: A

Concept

In a linear-equations word problem, translate every stated relation into an equation, then solve from the relation that involves the fewest unknowns first. A quantity is uniquely fixed once enough independent equations link it to known totals; substitute forward until every count is determined.

Setting up the equations

Let LA and P denote the number of lab assistants and professors in each college. The given relations are:

  1. A: LA(A) + P(A) = 82.

  2. B: LA(B) = LA(C) + 4.

  3. C: P(C) = LA(C) + 6.

  4. P(A) = LA(B) - 44.

  5. Total staff in C = total staff in A + 24.

  6. P(A) + P(B) + P(C) + P(D) = 102.

  7. Total staff in D : LA(A) = 3 : 4.

  8. LA(D) = LA(C) - 20.

Solving step by step

  1. Staff in A = 82, so staff in C = 82 + 24 = 106.

  2. In C, LA(C) + P(C) = 106 and P(C) = LA(C) + 6. Substituting: 2*LA(C) + 6 = 106, so LA(C) = 50 and P(C) = 56.

  3. LA(B) = LA(C) + 4 = 54, hence P(A) = LA(B) - 44 = 10.

  4. From LA(A) + P(A) = 82: LA(A) = 82 - 10 = 72.

  5. LA(D) = LA(C) - 20 = 30.

  6. Staff in D = (3/4)*LA(A) = (3/4)*72 = 54.

  7. Professors in D = staff in D - LA(D) = 54 - 30 = 24.

Cross-check

Total professors = P(A) + P(B) + P(C) + P(D). With P(A)=10, P(C)=56, P(D)=24, the total 102 forces P(B)=12, a consistent positive count. Every staff total (A=82, C=106) and the 3:4 ratio (54:72) hold, confirming professors in D = 24.

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