Correct Answer - Option 4 : 53658

**Concept used **

Divisibility rule of 99 : Number should be divisible by 9 and 11

Divisibility of 9 = sum of digit should be divisible by 9

Divisibility of 11 = Difference in sum of even place digit and sum of odd place digit is 0 or multiple of 11

**Calculation **

From option

Now option (1) 42767

⇒ 42767 = 4 + 2 + 7 + 6 + 7 = 27

27 is divisible by 9

Now check for 11

⇒ (4 + 7 + 7) - (2 + 6) = 10

10 is not divisible by 11

So number is not divisible by 99

Now option (2) 31781

⇒ 31781 = 3 + 7 + 1 + 8 + 1 = 20

20 is not divisible by 9

So number is not divisible by 99

Now Option (3) 21187

⇒ 21187 = 2 + 1 + 1 + 8 + 7 = 19

19 is not divisible by 9

So number is not divisible by 99

Now option (4)

⇒ 53658 = 5 + 3 + 6 + 5 + 8 = 27

27 is divisible by 9

Now check for divisibility of 11

⇒ (5 + 6 + 8) - (3 + 5) = 11

So, number is divisible by 99

**∴ 53658 is divisible by 99 **