The sequence of reactions involved are

CaCO₃ → CaO + CO₂ ...(1)

CaO + 3C → CaC₂ + CO ...(2)

CaC₂ + 2H₂O → C₂H₂ + Ca(OH)₂ ...(3)

Given

Moles of C₂H₂ formed = 2moles

starting from (3) equation

$$\begin{gathered} {\mathrm{CaC}}_2 +2{\mathrm{H}}_2\mathrm{O}\to {\mathrm{C}}_2{\mathrm{H}}_2 +\mathrm{Ca}{\left(\mathrm{OH}\right)}_2 \\ 1 \mathrm{mole} \mathrm{of} {\mathrm{CaC}}_{2 }-1 \mathrm{mole} \mathrm{of} {\mathrm{C}}_2{\mathrm{H}}_2 \\ {\mathrm{x}}_1 \mathrm{moles} \mathrm{of} {\mathrm{CaC}}_2 -2 \mathrm{moles} \mathrm{of} {\mathrm{C}}_2{\mathrm{H}}_2 \end{gathered}$$

X₁ = 2moles

2equation

$$\begin{gathered} \mathrm{CaO}+3\mathrm{C}\to {\mathrm{CaC}}_2 +\mathrm{CO} \\ 1 \mathrm{mole} \mathrm{of} \mathrm{CaO} -1 \mathrm{molof} {\mathrm{CaC}}_2 \\ {\mathrm{X}}_2 \mathrm{moles} \mathrm{of} \mathrm{CaO} -2 \mathrm{moles} \mathrm{of} {\mathrm{CaC}}_2 \end{gathered}$$

X₂ = 2moles

1st equation

$$\begin{gathered} {\mathrm{CaCO}}_3 \to \mathrm{CaO} +{\mathrm{CO}}_2 \\ 1 \mathrm{mole} \mathrm{of} {\mathrm{CaCO}}_3 -1 \mathrm{mole} \mathrm{of} \mathrm{CaO} \\ {\mathrm{X}}_3 \mathrm{mole} \mathrm{of} {\mathrm{CaCO}}_3 -{\mathrm{X}}_3 \mathrm{mole} \mathrm{of} \mathrm{CaO} \end{gathered}$$

X₃ = 2moles

Weight of pure CaCO₃ required =2$\times$100 =200 gm

Weight of 80% pure CaCO₃ required =200$\times$$\frac{100}{80}$= 250g