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Select the correct answerThe expenditure in a hostel is partly variable and directly proportional to the number of students, the rest being a fixed amount. If the expenditure were Rs.8400 for 120 students and Rs.10000 for 150 students, what would be the expenditure for 330 students?OptionsRs.19,600Rs.22,400Rs.18,000Rs.21,500

Question

Select the correct answerThe expenditure in a hostel is partly variable and directly proportional to the number of students, the rest being a fixed amount. If the expenditure were Rs.8400 for 120 students and Rs.10000 for 150 students, what would be the expenditure for 330 students?OptionsRs.19,600Rs.22,400Rs.18,000Rs.21,500

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Solution

To solve this problem, we need to establish the relationship between the number of students and the expenditure.

Given that the expenditure is partly variable and directly proportional to the number of students, we can express this relationship as E = kN + C, where E is the expenditure, N is the number of students, k is the constant of proportionality, and C is the fixed cost.

We have two equations based on the information provided:

  1. 8400 = 120k + C
  2. 10000 = 150k + C

Subtracting the first equation from the second gives us:

1600 = 30k

Solving for k, we find that k = 1600 / 30 = 53.33 (approx)

Substituting k = 53.33 into the first equation gives us:

8400 = 120*53.33 + C 8400 = 6400 + C C = 8400 - 6400 = 2000

So, the expenditure E for 330 students would be E = 53.33*330 + 2000 = Rs. 17,600 + 2000 = Rs. 19,600.

So, the correct answer is Rs.19,600.

This problem has been solved

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