The average of ten numbers is 7. If each number is multiplied by 12, then the average of the new set of numbers is :

Average of 10 numbers = 7
Sum of these 10 numbers = (10 × 7) = 70
$$\eqalign{ & \therefore {x_1} + {x_2} + ..... + {x_{10}} = 70 \cr & \Rightarrow 12{x_1} + 12{x_2} + ..... + 12{x_{10}} = 840 \cr & \Rightarrow \frac{{12{x_1} + 12{x_2} + ..... + 12{x_{10}}}}{{10}} = 84 \cr} $$
⇒ Average of new numbers is 84