Bihar Police Constable Model Paper 2

Given:
The average of 10 number is 6.
Concept:
Average = (Sum of all observation/number of observation)
Calculation:
Let the 10 number is ${\mathit{a}}_1,{\mathit{a}}_2,{\mathit{a}}_3$ . . . ${\mathit{a}}_{10}$
The average of 10 number is
⇒ $\frac{\left({\mathit{a}}_1+{\mathit{a}}_3+{\mathit{a}}_3+...+{\mathit{a}}_{10}\right)}{10}$
According to the question
⇒ $\frac{\left({\mathit{a}}_1+{\mathit{a}}_3+{\mathit{a}}_3+...+{\mathit{a}}_{10}\right)}{10}$ = 6
⇒$\left({\mathit{a}}_1+{\mathit{a}}_3+{\mathit{a}}_3+...+{\mathit{a}}_{10}\right)$ = 60 . . . (1)
Now,
Each number is multiplied by 13, then the new number is
$13{\mathit{a}}_1,13{\mathit{a}}_2,13{\mathit{a}}_3...13{\mathit{a}}_{10}$
So,
The average of the 10 new number is
⇒ $\frac{\left(13{\mathit{a}}_1+13{\mathit{a}}_3+13{\mathit{a}}_3+...+13{\mathit{a}}_{10}\right)}{10}$
⇒ $\frac{\left[13\left({\mathit{a}}_1+{\mathit{a}}_3+{\mathit{a}}_3+...+{\mathit{a}}_{10}\right)\right]}{10}$
⇒ (13 × 60)/10 . . . from equation (1)
⇒ 78
The required average is 78.