If the average of 6 consecutive even number is 25, the difference between the largest and the smallest number is :

According to the question,
Sum of 6 consecutive even number is = 25 × 6 = 150
Sn = $$\frac{n}{2}$$ [2a +(n - 1) × d]
⇒ 150 = $$\frac{6}{2}$$ [2a + (6 - 1) × 2]
⇒ 150 = $$\frac{6}{2}$$ (2a + 10)
⇒ 300 = 12a + 60
⇒ 12 a = 240
⇒ a = $$\frac{240}{12}$$
⇒ a = 20
∴ Numbers are 20, 22, 24, 26, 28, 30
Difference between largest and smallest is
= 30 - 20
= 10

Alternate :
Let the 6 consecutive number is
= x, x + 2, x + 4, x + 6, x + 8, x + 10
According to the question,
Largest number = Average + (n - 1) = 25 + 5 = 30
Smallest number = Average - (n - 1) = 25 - 5 = 20
Difference between largest and smallest number
= 30 - 20
= 10