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Q.

How many three-digit numbers are divisible by 9?


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a

96

b

90

c

86 

d

100

answer is A.

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Detailed Solution

The three-digit numbers divisible by 9 are 108,117,126,...,999.
Thus, a=108 and, d=117−108 ⇒d=9
T n =999
Formula for the nth term:
T n =a+ n−1 ×d
Applying,
108+(n−1)×9=999               ⇒9n+99=999 ⇒9n=999−99 ⇒9n=900
⇒n= 900 9 ⇒n=100
Therefore, there are 100 three-digit numbers divisible by 9.
Hence, option (1) is correct.
 
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