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The total income through the tuition fees of a management school has two components - the first component is fixed and the second component varies directly with the number of students. The average tuition fee per student is Rs. 5 lakhs when there are 30 students and Rs. 6 lakhs when there are 20 students. If the average tuition fee per student is Rs. 4 lakhs, how many students are there?

The total income through the tuition fees of a management school has two components - the first component is fixed and the second component varies directly with the number of students. The average tuition fee per student is Rs. 5 lakhs when there are 30 students and Rs. 6 lakhs when there are 20 students. If the average tuition fee per student is Rs. 4 lakhs, how many students are there? Correct Answer 60

Suppose the fixed component is ‘x’ and the variable component is ‘y’ per student

x + 30y = (30 × 5)

⇒ x + 30y = 150 lakhs      ----(1)

⇒ x + 20y = (20 × 6)

⇒ x + 20y = 120 lakhs      ----(2)

⇒ x + 20y = 120 lakhs

Solving Equation 1 and 2, we get x = 60 lakhs, b = 3 lakhs

Let the number of students be ‘a’

Average fee per student = Rs. 4 lakhs

Total fees = 4a = 60 + 3a

⇒ 4a - 3a = 60

⇒ a = 60

∴ Number of students = 60

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