Question

The mean of eleven numbers is $47.$ If a number is added then the mean is increased by $2.$ Find the new number.

Answer 1

The mean of eleven numbers is $47.$
The sum of $11$ numbers $=11\times 47=517$
Let the new number added be $x.$
The new mean of $12$ numbers is $=47+2=49$
The sum of $12$ numbers $=49\times 12=588$
$$\begin{gathered} \Rightarrow 517+x=588 \\ \Rightarrow x=588-517 \\ \Rightarrow x=71 \end{gathered}$$
Hence, the value of $x$ is $71$