Question

The average of 31 persons of a group is 19 years. If a person is excluded, the average becomes 18 years. Find the age of excluded person.

Answer 1

 Simple method :

Sum of the ages of 31 persons $=31 \times 19=589$ years

Sum of the ages of 30 persons $=30 \times 18=540$ years

$\therefore$ The age of excluded person $=589-540=49$ years; Ans.

Trick:

Required age

$$

\begin{array}{l}

=19-\frac{31-1}{1} \times(18-19) \\

=19+30 \times 1=49 ; \text { years; Ans. }

\end{array}

$$