Question

How many numbers between 99 to 999 which are divisible by 11 . 
1. 82
2. 81
3. 83
4. 80

Answer 1

Correct Answer - Option 2 : 81

Concept:

nth  term of A.P are a, a + d , a + 2d,  . . . .  ,a + (n-1)d .

Tn  = a + ( n - 1 ) d 

Where a = first term and d = common difference 

Calculation :

The series are given as 110, 121,.... 990 .

Here , a = 110 , d = 11 , Tn = 990

we know that , Tn = a + ( n - 1 ) d  

⇒ 990 = 110 + ( n - 1 ) × 11 

⇒ 880 = ( n - 1) × 11

⇒ 80 = n - 1 

⇒ n = 81

The correct option is 2.