There are three categories of jobs A, B and C. The average salary of the student 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 is 34 lakh per annum. The most appropriate (or closet) 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):

Explanation:-

$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{number}}\,{\text{of}}\,{\text{students}}\,{\text{who}}\,{\text{got}}\,{\text{the}}\,{\text{job}}\,{\text{of}} \cr & \,A,\,B\,{\text{and}}\,C\,{\text{categories}}\,{\text{is}}\,{\text{a,}}\,{\text{b}}\,{\text{and}}\,{\text{c}}\,{\text{respectively}}, \cr & {\text{Then}}\,{\text{the}}\,{\text{total}}\,{\text{salary}}, \cr & = \left[ {\frac{{\left\{ {26\left( {a + b} \right) + 44\left( {b + c} \right) + 34\left( {c + a} \right)} \right\}}}{{2\left( {a + b + c} \right)}}} \right] \cr & = \left[ {\frac{{\left( {60a + 70b + 78c} \right)}}{{2\left( {a + b + c} \right)}}} \right] \cr & = \frac{{\left[ {30\left( {a + b + c} \right) + \left( {5b + 9c} \right)} \right]}}{{\left( {a + b + c} \right)}} \cr & = 30 + {\text{some}}\,{\text{positive}}\,{\text{value}} \cr & {\text{Thus,}}\,{\text{the}}\,{\text{minimum}}\,{\text{salary}}\,{\text{must}}\,{\text{be}}\,Rs.\,30\,l{\text{akh}}\,{\text{and}} \cr & {\text{the}}\,{\text{maximum}}\,{\text{salary}}\,{\text{can}}\,{\text{not}}\,{\text{exceed}}\,44, \cr & {\text{which}}\,{\text{is}}\,{\text{the}}\,{\text{highest}}\,{\text{of}}\,{\text{the}}\,{\text{three}} \cr}$$