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$$\begin{gathered} \mathrm{Let} \mathrm{the} \mathrm{number} \mathrm{of} \mathrm{diamond} \mathrm{stones} \mathrm{serena} \mathrm{had} = \mathrm{x} \\ \mathrm{Number} \mathrm{of} \mathrm{diamond} \mathrm{stones} \mathrm{john} \mathrm{had} = \left(45-\mathrm{x}\right) \\ \mathrm{Now}, \\ \mathrm{They} \mathrm{sold} 5 \mathrm{stones} \mathrm{each}. \\ \mathrm{Number} \mathrm{of} \mathrm{diamond} \mathrm{stones} \mathrm{now} \mathrm{serena} \mathrm{have}=\left(\mathrm{x}-5\right) \\ \mathrm{Number} \mathrm{of} \mathrm{diamond} \mathrm{stones} \mathrm{now} \mathrm{john} \mathrm{have}=\left(45-\mathrm{x}-5\right)=\left(40-\mathrm{x}\right) \\ \mathrm{Product} \mathrm{of} \mathrm{remaining} \mathrm{stones}=124 \\ \left(\mathrm{x}-5\right) \left(40-\mathrm{x}\right)=124 \\ 40\mathrm{x}-{\mathrm{x}}^2-200+5\mathrm{x}=124 \\ -{\mathrm{x}}^2+45\mathrm{x}-200-124=0 \\ -{\mathrm{x}}^2+45\mathrm{x}-324=0 \\ {\mathrm{x}}^2-45\mathrm{x}+324=0 \\ {\mathrm{x}}^2-36\mathrm{x}-9\mathrm{x}+324=0 \\ \mathrm{x} \left(\mathrm{x}-36\right) -9 \left(\mathrm{x}-36\right)=0 \\ \left(\mathrm{x}-9\right) \left(\mathrm{x}-36\right)=0 \\ \mathrm{x}-9=0 \mathrm{or} \mathrm{x}-36=0 \\ \mathrm{x}=9 \mathrm{or} \mathrm{x}=36 \\ \mathrm{Case}-\mathrm{I} \\ \mathrm{x}=9 \\ \mathrm{Serena} \mathrm{had} 9 \mathrm{stones} \mathrm{and} \mathrm{john} \mathrm{had} 36 \mathrm{stones}. \\ \mathrm{Case}-\mathrm{II} \\ \mathrm{x}=36 \\ \mathrm{Serena} \mathrm{had} 36 \mathrm{stones} \mathrm{and} \mathrm{john} \mathrm{had} 9 \mathrm{stones}. \end{gathered}$$

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