\\(\\begin{array}{l}{\ ext { (i) Let the number of John's marbles be } x \ ext { . }} \\\\ {\ ext { The refore, number of Jivanti's marble }=45-x} \\\\ {\ ext { After losing } 5 \ ext { marbles, }} \\\\ {\ ext { Number of John's marbles = } x-5} \\\\ {\ ext { Number of Jivanti's marbles = } 45-x-5=40-x} \\\\ {\ ext { It is given that the product of their marbles is } 124 .}\\end{array}\\)
\\(\\begin{array}{l}{\ herefore(x-5)(40-x)=124} \\\\ {\\Rightarrow x^{2}-45 x+324=0} \\\\ {\\Rightarrow x^{2}-36 x-9 x+324=0} \\\\ {\\Rightarrow x(x-36)-9(x-36)=0} \\\\ {\\Rightarrow(x-36)(x-9)=0}\\end{array}\\)
\\(\\begin{array}{l}{\ ext { Either } x-36=0 \ ext { or } x-9=0} \\\\ {\ ext { i.e., } x=36 \ ext { or } x=9} \\\\ {\ ext { If the number of John's marbles }=36 \ ext { , }} \\\\ {\ ext { Then, number of Jivanti's marbles }=45-36=9} \\\\ {\ ext { If number of John's marbles }=9,} \\\\ {\ ext { Then, number of Jivanti's marbles }=45-9=36}\\end{array}\\)
\\(\\begin{array}{l}{\ ext { (ii) Let the number of toys produced be } x \ ext { . }} \\\\ {\ herefore \ ext { cost of production of each toy }=R s(55-x)} \\\\ {\ ext { It is given that, total production of the toys }=Rs 750}\\end{array}\\)
\\(\\begin{array}{l}{\ herefore x(55-x)=750} \\\\ {\\Rightarrow x^{2}-55 x+750=0} \\\\ {\\Rightarrow x^{2}-25 x-30 x+750=0} \\\\ {\\Rightarrow x(x-25)-30(x-25)=0} \\\\ {\\Rightarrow(x-25)(x-30)=0}\\end{array}\\)
\\( \\begin{array}{l}{\ ext { Either } x-25=0 \ ext { or } x-30=0} \\\\ {\ ext { i.e., } x=25 \ ext { or } x=30} \\\\ {\ ext { Hence, the number of toys will be either } 25 \ ext { or } 30 \ ext { . }}\\end{array}\\)