There are three categories of jobs A,B and c . The average salary of the students who got the job of A and B categories is 26 lakh per annum. The average salary of the students who got the job of B and C category is 44 lakh per annum and the average salary of those students who got the job of A and C categories 34 lakh per annum. The most appropriate (or closest) range of average salary of all the three categories (if it is known that each student gets only one category of jobs i.e, A, B and C):

Options

A. Lies between 30 and 40
B. lies between 28 and 34
C. lies between 34 and 43
D. lies between 29 and 48

Answer

To solve the problem, we need to find the average salary of three job categories A, B, and C based on the given average salaries of pairs of categories.

Let's denote:
- The average salary of category A as \( A \)
- The average salary of category B as \( B \)
- The average salary of category C as \( C \)

We have the following information from the question:

1. The average salary of students who got jobs in categories A and B is 26 lakh per annum:
\[ \frac{A + B}{2} = 26 \implies A + B = 52 \quad \text{(Equation 1)} \]

2. The average salary of students who got jobs in categories B and C is 44 lakh per annum:
\[ \frac{B + C}{2} = 44 \implies B + C = 88 \quad \text{(Equation 2)} \]

3. The average salary of students who got jobs in categories A and C is 34 lakh per annum:
\[ \frac{A + C}{2} = 34 \implies A + C = 68 \quad \text{(Equation 3)} \]

Now, we have a system of three equations:
1. \( A + B = 52 \)
2. \( B + C = 88 \)
3. \( A + C = 68 \)

### Step 1: Solve the equations

We can solve these equations step by step.

From Equation 1, we can express \( B \) in terms of \( A \):
\[ B = 52 - A \quad \text{(Equation 4)} \]

Substituting Equation 4 into Equation 2:
\[ (52 - A) + C = 88 \]
\[ C = 88 - 52 + A = 36 + A \quad \text{(Equation 5)} \]

Now, substitute Equation 5 into Equation 3:
\[ A + (36 + A) = 68 \]
\[ 2A + 36 = 68 \]
\[ 2A = 68 - 36 \]
\[ 2A = 32 \implies A = 16 \]

### Step 2: Find B and C

Now that we have \( A \), we can find \( B \) and \( C \) using Equations 4 and 5.

Substituting \( A = 16 \) into Equation 4:
\[ B = 52 - 16 = 36 \]

Substituting \( A = 16 \) into Equation 5:
\[ C = 36 + 16 = 52 \]

### Step 3: Calculate the average salary of all three categories

Now we have:
- \( A = 16 \) lakh
- \( B = 36 \) lakh
- \( C = 52 \) lakh

To find the average salary of all three categories:
\[ \text{Average} = \frac{A + B + C}{3} = \frac{16 + 36 + 52}{3} = \frac{104}{3} \approx 34.67 \text{ lakh} \]

### Conclusion

The average salary of all three categories is approximately 34.67 lakh per annum.