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.

Total professor in A is what percentage of total staff in B.

The correct answer is 11.11%.

Let the number of lab assistants in colleges A, B, and C be represented by $L_A$, $L_B$, and $L_C$, and the number of professors be represented by $P_A$, $P_B$, and $P_C$ respectively.

From the given information, we can set up the following steps to find the values:

Step 1: Find the total staff in college C
We are given that the total staff (lab assistants + professors) in college A is 82:
$L_A+P_A=82$
The total staff in college C is 24 more than that in college A:
$\text{Total staff in C}=82+24=106$
So,
$L_C+P_C=106$

Step 2: Find the number of lab assistants and professors in college C
For college C, the total lab assistants is 6 less than the total professors:
$L_C=P_C-6$
⇒ $P_C=L_C+6$
Substituting this value into the total staff equation for C:
$L_C+(L_C+6)=106$
$2L_C+6=106$
$2L_C=100$
$L_C=50$
Therefore, the number of professors in college C is:
$P_C=50+6=56$

Step 3: Find the number of lab assistants in college B
The lab assistants in college B is 4 more than the lab assistants in C:
$L_B=L_C+4=50+4=54$

Step 4: Find the number of professors in college A
The number of professors in college A is 44 less than the lab assistants in college B:
$P_A=L_B-44=54-44=10$

Step 5: Find the number of professors in college B
The total number of professors in all three colleges is 102:
$P_A+P_B+P_C=102$
Substituting the known values:
$10+P_B+56=102$
$66+P_B=102$
$P_B=36$

Step 6: Find the total staff in college B
The total staff in college B is the sum of its lab assistants and professors:
$\text{Total staff in B}=L_B+P_B=54+36=90$

Step 7: Calculate the required percentage
We need to find what percentage of the total staff in B is the total professors in A:
$\text{Percentage}=\left(\frac{P_A}{\text{Total staff in B}}\right)\times 100$
$\text{Percentage}=\left(\frac{10}{90}\right)\times 100=\frac{100}{9}\%\approx 11.11\%$