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 in 10 innings (A=60, N=10)

⇒S=60 X 10 =600

Later, In how many runs are to be scored in the 11 innings to raise the mean score to 62 (so A=62, N=11)

So, sum of 7 observations

⇒S=62 X 11 =682

Now,

Score of 11th innings =(sum of runs in 10 innings)-(Sum of runs in 11 innings)

=682-600

= 82

Hence, Option D is correct.