The mean of 5, 7, 8, 4 and m is n and the mean of 5, 7, 8, 4, m and n is m. Find the values of m and n.

Given,

The mean of 5, 7, 8, 4 and m is n.

$\therefore \dfrac{5 + 7 + 8 + 4 + m}{5} = n \\[1em] \Rightarrow m + 24 = 5n \\[1em] \Rightarrow m = 5n - 24 \text{ ………(1)}$

The mean of 5, 7, 8, 4, m and n is m.

$\therefore \dfrac{5 + 7 + 8 + 4 + m + n}{6} = m \\[1em] \Rightarrow m + n + 24 = 6m$

Substituting value of m from equation (1) in above equation, we get :

⇒ 5n - 24 + n + 24 = 6m

⇒ 6n = 6m

⇒ n = m ………(2)

Substituting value of n from equation (2) in (1), we get :

⇒ m = 5m - 24

⇒ 5m - m = 24

⇒ 4m = 24

⇒ m = $\dfrac{24}{4}$ = 6

⇒ n = 6.

Hence, m = 6 and n = 6.