An LGA has a population of $250{,}000$. The constitution requires that each councilor represent no more than $20{,}000$ persons. The LGA currently has 8 councilors. The state proposes to increase the number of councilors by a fixed integer $k$ so that the representation ratio meets the constitutional limit, and to allocate a total annual budget of \text{₦}120 million, where each councilor receives an equal allowance of \text{₦}1.5 million and the remaining budget funds development projects.

Determine the minimum integer $k$, the total number of councilors after the increase, the amount allocated to development projects (in millions of naira), and state whether the new arrangement satisfies the constitutional representation requirement.

Question

An LGA has a population of $250{,}000$. The constitution requires that each councilor represent no more than $20{,}000$ persons. The LGA currently has 8 councilors. The state proposes to increase the number of councilors by a fixed integer $k$ so that the representation ratio meets the constitutional limit, and to allocate a total annual budget of \text{₦}120 million, where each councilor receives an equal allowance of \text{₦}1.5 million and the remaining budget funds development projects.

Determine the minimum integer $k$, the total number of councilors after the increase, the amount allocated to development projects (in millions of naira), and state whether the new arrangement satisfies the constitutional representation requirement.

Accepted Answer

k = 5; total councilors = 13; development allocation = ₦100.5 million; constitutional requirement satisfied

Neco 2019 Government Question 39

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