Choose the correct answer in each of the following questions:

Let a be the first term and d be the common difference of the AP. Then,

$a_{5}=20$

$\Rightarrow a+(5-1) d=20 \quad\left[a_{n}=a+(n-1) d\right]$

$\Rightarrow a+4 d=20 \quad \ldots .(1)$

Now,

$a_{7}+a_{11}=64$              (Given)

$\Rightarrow(a+6 d)+(a+10 d)=64$

$\Rightarrow 2 a+16 d=64$

$\Rightarrow a+8 d=32 \quad \ldots(2)$

From (1) and (2), we get

$20-4 d+8 d=32$

$\Rightarrow 4 d=32-20=12$

$\Rightarrow d=3$

Thus, the common difference of the AP is 3.

Hence, the correct answer is option C.