$\begin{array}{1,1}(a)\;424.67\times10^4g\\(b)\;4.2467\times10^4g\\(c)\;42.467\times10^4g\\(d)\;0.424\times10^4g \end {array}$

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Weight of balloon = 100 kg or $10\times10^4g$

Volume of balloon = $\large\frac{4}{3}\pi r^3$

$\;\;\;\;\;\;\;\;\;= \large\frac{4}{3}\times\large\frac{22}{7}\times(\large\frac{20}{2}\times100)^3$

$\;\;\;\;\;\;\;\;\;=4190\times10^6cm^3$

$\;\;\;\;\;\;\;\;\;=4190\times10^3\;litre$

Weight of gas (He) in balloon = $\large\frac{PV_m}{RT}$

(Since PV = $\large\frac{w}{m}RT$)

$=\large\frac{1\times4190\times10^3\times4}{0.082\times300}$

$=68.17\times10^4g$

$\therefore$ Total weight of gas and balloon = $68.13\times10^4+10\times10^4 = 78.13\times10^4$

Weight of air displaced = $\large\frac{1.2\times4190\times10^6}{10^3}$

$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;= 502.8\times10^4g$

$\therefore$ Pay load = weight of air displaced - (weight of balloon + weight of gas)

$\therefore$ Pay load = $502.8\times10^4 - 78.13\times10^4$

$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;=424.67\times10^4g$

Hence answer is (A)

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