Calculate Total Monthly Salary of Professors in University F

This question asks us to find the total monthly salary of a specific group of teachers (Professors) from one university (University F), based on percentage distribution data for teachers across six different universities (A to F).

Understanding the Provided Data

We are given a table showing the percentage of teachers in each university out of the total number of teachers across all six universities. We are also given the exact number of teachers in University E is 1856.

Additionally, we know that 1/36th of the teachers in University F are Professors, and each Professor earns ₹96000 per month.

Steps to Solve the Problem

1. Determine the total number of teachers across all six universities using the information for University E.
2. Calculate the total number of teachers specifically in University F based on the percentage distribution.
3. Find the number of Professors in University F.
4. Calculate the total monthly salary by multiplying the number of Professors by the salary per Professor.

Detailed Calculation Steps

Step 1: Find the Total Number of Teachers (All Universities)

We are told that 29% of the total teachers are in University E, and there are 1856 teachers in E.

Let \(T_{total}\) be the total number of teachers in all six universities.

\(29\%\) of \(T_{total} = 1856\)

This can be written as:

\(\frac{29}{100} \times T_{total} = 1856\)

Now, we solve for \(T_{total}\):

\(T_{total} = \frac{1856 \times 100}{29}\)

\(T_{total} = \frac{185600}{29}\)

\(T_{total} = 6400\)

So, there are 6400 teachers in total across all universities.

Step 2: Find the Number of Teachers in University F

According to the table, 18% of the total teachers are in University F.

Number of teachers in University F = \(18\%\) of \(T_{total}\)

= \(18\%\) of \(6400\)

= \(\frac{18}{100} \times 6400\)

= \(0.18 \times 6400\)

= \(1152\)

There are 1152 teachers in University F.

Step 3: Find the Number of Professors in University F

The problem states that 1/36th of the teachers in University F are Professors.

Number of Professors in F = \(\frac{1}{36} \times (\text{Number of teachers in F})\)

= \(\frac{1}{36} \times 1152\)

= \(\frac{1152}{36}\)

= \(32\)

There are 32 Professors in University F.

Step 4: Calculate the Total Monthly Salary of Professors in F

Each Professor receives a salary of ₹96000 per month.

Total monthly salary = (Number of Professors in F) \(\times\) (Salary per Professor)

= \(32 \times 96000\)

= \(3072000\)

The total monthly salary for the Professors in University F is ₹3072000.

The options are given in lakhs. To convert ₹3072000 to lakhs, we divide by 100,000 (since 1 lakh = ₹100,000).

\(\frac{3072000}{100000} = 30.72\)

So, the total monthly salary is ₹30.72 lakh.

Based on our calculations, the total monthly salary of all these Professors from University F is ₹30.72 lakh.

Revision Table: Summary of Teacher and Salary Calculation

Additional Information: Data Interpretation and Percentage Calculations

Data interpretation questions often require you to combine information from different parts of the question or table to arrive at the solution. Understanding percentages and how to calculate with them is crucial.

• Percentage Basics: A percentage is a fraction out of 100. \(X\%\) means \(\frac{X}{100}\).
• Finding the Whole from a Part: If you know that a certain number represents a percentage of a total, you can find the total. For example, if \(Y\) is \(X\%\) of a total \(Z\), then \(Y = \frac{X}{100} \times Z\), so \(Z = \frac{Y \times 100}{X}\). This is what we did to find the total number of teachers.
• Finding a Part from the Whole: If you know the total and the percentage of a part, you can find the number representing that part. For example, if you want to find \(X\%\) of a total \(Z\), you calculate \(\frac{X}{100} \times Z\). This was used to find the number of teachers in University F.
• Fractions: Fractions like 1/36 represent a portion of a whole. To find that portion, you multiply the fraction by the whole number.
• Units and Conversion: Always pay attention to the units given (e.g., absolute numbers, percentages, currency). Be prepared to convert between units, such as converting rupees to lakhs as required by the answer options. 1 lakh = 100,000.

Practicing various data interpretation sets will help you become comfortable with these calculations and interpretations.