Rate law for the reaction,

2A + B $$ \to $$ C

Rate law (R) = k[A]^x[B]^y

From experiment 1 :

R₁ = 0.045 = k[0.05]^x [0.05]^y ............(i)

From experiment 2 :

R₂ = 0.090 = k[0.1]^x [0.05]^y ...............(ii)

From experiment 3 :

R₃ = 0.72 = k[0.2]^x [0.1]^y ...................(iii)

Divide equation (ii) by equation (i),

$${{{R_2}} \over {{R_1}}} = {{0.09} \over {0.045}} = {{k{{\left[ {0.1} \right]}^x}{{\left[ {0.05} \right]}^y}} \over {k{{\left[ {0.05} \right]}^x}{{\left[ {0.05} \right]}^y}}}$$

$$ \Rightarrow $$ 2 = (2)^x

$$ \Rightarrow $$ x = 1

Divide equation (iii) by equation (ii),

$${{{R_3}} \over {{R_2}}} = {{0.72} \over {0.09}} = {{k{{\left[ {0.2} \right]}^x}{{\left[ {0.1} \right]}^y}} \over {k{{\left[ {0.1} \right]}^x}{{\left[ {0.05} \right]}^y}}}$$

$$ \Rightarrow $$ 8 = 2^x 2^y

$$ \Rightarrow $$ 8 = 2¹ 2^y [as x = 1]

$$ \Rightarrow $$ 2^y = 4

$$ \Rightarrow $$ y = 2

$$ \therefore $$ Rate law (R) = k[A]¹[B]²