Here we can use the formula

$$\begin{gathered} \text{Average (A)=}\frac{\mathrm{Sum} \mathrm{of} \mathrm{observations} \left(\mathrm{S}\right)}{\mathrm{No}. \mathrm{of} \mathrm{observations} \left(\mathrm{N}\right)} \\ \text{⇒ S=A×N} \end{gathered}$$

According to the question,

Sum of runs scored in 15 innings (A=45, N=15)

⇒S=45 X 15 =675

Later, The runs average becomes 47, after 18 innings. (so A=47, N=18)

So, sum of runs scored in 18 innings

⇒S=47 X 18 =846

Now,

Runs scored in 20 innings =(sum of runs scored in 15 innings)-(Sum of runs scored in 18 innings)

=846-675

=171

Hence, Option B is correct.