The mean of 5 numbers is 27 if one number is excluded their mean is 25

1.	The mean of 5 numbers is 27 if one number is excluded their mean is 25 find the excluded number
Answer» $\mathfrak{\large{\underline{\underline{\pink{Answer :-}}}}}$ The Excluded number is 47 $\mathfrak{\large{\underline{\underline{\pink{Explanation :-}}}}}$ Given : Mean of 5 NUMBERS = 27 ONE number excluded the new mean = 25 To FIND : The Excluded number Solution : $\textbf{Case I}$ Here, Mean = 27 Observations = 5 Sum of Observations = x ★ $\boxed{\sf{\purple{Mean = \frac{Sum \: of \: Observations}{No. \: of \: Observations}}}}$ $\sf{\implies} \: 27 = \dfrac{x}{5}$ $\sf{\implies} \: 27 \times 5 = x$ $\sf{\implies} \: x = 135$ Sum of Observations in Case I is 135 $\rule{300}{1.5}$ $\textbf{Case II}$ Here, Mean = 22 Observations = 4 (one number Excluded) Consider Excluded number as y Sum of Observations = 135 - y ★ $\boxed{\sf{\purple{Mean = \frac{Sum \: of \: Observations}{No. \: of \: Observations}}}}$ $\sf{\implies} \:22 = \dfrac{135 - y}{4}$ $\sf{\implies} \:22 \times 4 = 135 - y$ $\sf{\implies} \:88 = 135 - y$ $\sf{\implies} \:y= 135 - 88$ $\sf{\implies} \:y = 47$ $\therefore$ The Excluded number is 47.