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