Read the information and answer the following question given below.

The information is about the staffs (lab assistant and professor) in three colleges.
For A – total lab assistant and total professor is 82.
For B – total lab assistant is 4 more than total lab assistant in C.
For C – total lab assistant is 6 less than total professor
Note – total professor in A is 44 less than total lab assistant in B.
Total staffs in C is 24 more than that in A and total professor in al the college is 102.

Find the total staff in B.

Correct Answer: Option 90

Let us break down the given information step-by-step to find the total staff in College B.

Let the number of lab assistants and professors in colleges A, B, and C be represented as follows:
- College A: $L_A$ (lab assistants) and $P_A$ (professors)
- College B: $L_B$ (lab assistants) and $P_B$ (professors)
- College C: $L_C$ (lab assistants) and $P_C$ (professors)

Step 1: Find the total staff in College C.
We are given that the total staff (lab assistants + professors) in College A is 82:
$S_A=L_A+P_A=82$
The total staff in College C is 24 more than that in College A:
$S_C=S_A+24=82+24=106$

Step 2: Find the number of lab assistants and professors in College C.
We know that in College C, the total number of lab assistants is 6 less than the total number of professors:
$L_C=P_C-6$ (or $P_C=L_C+6$)
Using the total staff equation for College C:
$L_C+P_C=106$
Substitute $P_C$ in the equation:
$L_C+(L_C+6)=106$
$2L_C+6=106$
$2L_C=100$
$L_C=50$
Now, find the number of professors in College C:
$P_C=50+6=56$

Step 3: Find the number of lab assistants in College B and professors in College A.
The number of lab assistants in B is 4 more than that in C:
$L_B=L_C+4=50+4=54$
The number of professors in A is 44 less than the lab assistants in B:
$P_A=L_B-44=54-44=10$

Step 4: Find the number of professors in College B.
The total number of professors in all three colleges is 102:
$P_A+P_B+P_C=102$
Substitute the values of $P_A$ and $P_C$:
$10+P_B+56=102$
$66+P_B=102$
$P_B=102-66=36$

Step 5: Calculate the total staff in College B.
The total staff in College B is the sum of its lab assistants and professors:
$S_B=L_B+P_B=54+36=90$

Thus, the total staff in B is 90.