$1/n_{CH_4}=20,16/22,4=0,9mol$
$CH_4+2O_2\overset{t^o}\to CO_2+2H_2O$
$\text{Theo pt :}$
$n_{O_2}=2.n_{CH_4}=2.0,9=1,8mol$
$⇒V_{O_2}=1,8.22,4=40,32g$
$2/n_{MnO_2}=8,7/87=0,1mol$
$2KMnO_4\overset{t^o}\to K_2MnO_4+MnO_2+O_2$
$\text{a/Theo pt :}$
$n_{KMnO_4}=2.n_{MnO_2}=2.0,1=0,2mol$
$⇒m_{KMnO_4}=0,2.158=31,6g$
$\text{b/Theo pt :}$
$n_{O_2}=n_{MnO_2}=0,1mol$
$⇒V_{O_2}=0,1.22,4=2,24l$