We need to check the number of values of $p$ for which the mean of the set $$30,40 \& p$$ is same as its median.

We know that mean is same as the median when numbers are consecutive or are in arithmetic sequence (Arithmetic sequence is a sequence in which consecutive terms have same gap between them, for example $$\mathrm{a}, \mathrm{a}+\mathrm{d}, \mathrm{a}+2 \mathrm{~d}, \mathrm{a}+3 \mathrm{~d} \&$$ so on).

The numbers $$30,40 \& p$$ can form an arithmetic sequence if $$x=20$$ or $$x=35$$ or $$x=50$$.

Thus, for the above three values of p , the numbers $$30,40 \& \mathrm{p}$$ will have same gap, so are the possible values of $$p$$.

Hence options (D) \& (E) are correct.