The average of three numbers is $40$. The first number is twice the second and the second one is thrice the third number. The difference between the largest and the smallest numbers is

The correct option is C $60$
Let the third number be $x$.
Then, second number be $=3x$
First number be $=2\times 3x=6x$
Given that,
Average of three numbers $=40$
Sum of three numbers $=40\times 3=120$
According to the question,
$x+3x+6x=120$
$10x=120$
$x=12$
Difference between largest and smallest numbers
$=6x-x=5x=5\times 12=60$.