The mean of a frequency distribution is $8.1$. If $\sum f_i{x}_i=132+5k$ and $\sum f_i=20$, then the value of $k$ is

The formula for the mean ($\bar{x}$) of a grouped frequency distribution is:
$$\bar{x}=\frac{\sum f_i{x}_i}{\sum f_i}$$

Substitute the given parameters into this equation:

$$8.1=\frac{132+5k}{20}$$

$$8.1\times 20=132+5k$$

$$162=132+5k$$

$$5k=162-132$$

$$5k=30⟹k=6$$