Question

Q1.The mean of six numbers is 20. If one of the numbers is excluded, the average is 8. Find out
the excluded number.
A. 12
B. 22
C. 80
D. 120​

Answer 1

Step-by-step explanation:

Mean of six terms = 20

$\begin{gathered} \rm \longrightarrow \dfrac{x_1 + x_2 + x_3...x_6}{6} = 20 \\ \\ \rm \longrightarrow {x_1 + x_2 + x_3...x_6} = 20 \times 6\\ \\ \rm \longrightarrow {x_1 + x_2 + x_3...x_6} = 120\end{gathered} </p><p></p><p> </p><p>$

$\rm \longrightarrow {x_1 + x_2 + x_3...x_6}$

If one of the numbers is excluded, the average is = 8

$\begin{gathered}\rm \longrightarrow \dfrac{x_1 + x_2 + x_3...x_5}{5} = 8 \\ \\ \rm \longrightarrow {x_1 + x_2 + x_3...x_5} = 8 \times 5\\ \\ \rm \longrightarrow {x_1 + x_2 + x_3...x_5} =40\end{gathered} </p><p>$

$\rm \longrightarrow {x_1 + x_2 + x_3...x_5} =s_ b=40</p><p>$

$\begin{gathered} \rm \longrightarrow Excluded \: number = s_ a -s_ b \\ \\ \rm \longrightarrow Excluded \: number = 120 -40\\ \\ \rm \longrightarrow Excluded \: number = 80\end{gathered} </p><p></p><p>$

Therefore, option (c) 80 is correct