Solutions
Divisibility rule of 9:
A number is divisible by 9 only when the sum of its digits is divisible by 9.
10098 → 1 + 0 + 0 + 9 + 8 = 18
10108 → 1 + 0 + 1 + 0 + 8 = 10
10089 → 1 + 0 + 0 + 8 + 9 = 18
10087 → 1 + 0 + 0 + 8 + 7 = 16
10098 and 10089 are the numbers that satisfy the condition
Divisibility rule of 11:
A number is divisible by 11 if the difference between the sum of its digits at odd places and the sum of its digits at even places is either 0 or a number divisible by 11
In case of 10098
⇒ (1 + 0 + 8) – (0 + 9) = 9 – 9 = 0 (Satisfying the condition)
Checking second term 10089
⇒ (1 + 0 + 9) – (0 + 8) = 9 – 8 = 1 (Not satisfying the condition)
∴ The number which is divisible by both 9 and 11 is 10098.