Neco Model Questions Vol1 2021 Government Question 44

In a mixed‑member proportional electoral system a legislature has \(100\) seats, of which \(70\) are constituency seats filled by first‑past‑the‑post and \(30\) are list seats used to achieve overall proportionality. Five parties obtain the following vote shares and constituency seats:\n\[\begin{array}{lccc}\text{Party}&\text{Vote \%}&\text{Constituency seats}\\\hline\text{P1}&40\%&45\\\text{P2}&30\%&20\\\text{P3}&20\%&5\\\text{P4}&5\%&0\\\text{P5}&5\%&0\end{array}\]\]\nA party must receive at least \(5\%\) of the vote to qualify for list seats. Compute the total number of seats in the legislature after accounting for any overhang seats that arise when a party wins more constituency seats than its proportional entitlement.