Question

The AM of $9$ terms is $15$. If one more term is added to this series, then AM becomes $16$. The value of the added term is.

• A. $30$
• B. $27$
• C. $25$
• D. $23$
• E. $20$

Answer 1

The correct option is C

$25$

Step 1: Given data

Arithmetic mean of $9$ term =$15$

Arithmetic mean after adding one term = $16$

Step 2: Formula used

It is understood that the arithmetic mean$\left(\overline{x}\right)=\frac{Sumofobservation}{Numberofobservation}$

Step 3: Compute the sum of nine terms

First, find the sum of 15 observations

$\begin{array}{rcl}\left(\overline{x}\right)& =& \frac{Sumofobservation}{Numberofobservation}\\ 15& =& \frac{Sumofobservation}{9}\\ 135& =& Sumofobservation\end{array}$

Thus, the sum of 15 observations is $135$.

Step 4: Determine the value of the new item

Suppose the new term is $t$. So,

$\begin{array}{rcl}\left(\overline{x}\right)& =& \frac{sumofnineterm+newterm}{Numberofobservation}\\ 16& =& \frac{135+t}{10}\\ 160& =& 135+t\\ t& =& 25\end{array}$

So, the value of the added term is $25$.

Hence, option C is the correct answer.