JAMB Mathematics 2019 Paper

Concept:When one quantity varies directly with one variable and inversely with another, combine both into a single constant equation.Explanation:Since $M$ varies directly as $N$ and inversely as $\sqrt{P}$, we write $M \propto \frac{N}{\sqrt{P}}$.Introduce the constant $k$: $M = \frac{kN}{\sqrt{P}}$.Substitute the given values $M=3$, $N=5$, and $P=25$: $3 = \frac{k(5)}{\sqrt{25}}$.Simplify: $3 = \frac{5k}{5}$, so $k = 3$.The relationship is now $M = \frac{3N}{\sqrt{P}}$.Use the new values $M=2$ and $N=6$: $2 = \frac{3(6)}{\sqrt{P}} = \frac{18}{\sqrt{P}}$.Solve for $\sqrt{P}$: $\sqrt{P} = \frac{18}{2} = 9$.Square both sides to eliminate the root: $P = 9^2 = 81$.Answer:$P = 81$, which is option D.