How many numbers are divisible by 9 in between 1 and 1000 ? A) 100 B

1.	How many numbers are divisible by 9 in between 1 and 1000 ? A) 100 B) 101 C) 110 D) 111
Answer» Correct option is (D) 111 First number between 1 & 1000 which is divisible by 9 is 9 & last number between 1 & 1000 which is divisible by 9 is 999. i.e., \(a_1=a=9\;\&\;a_n=999,d=9\) \(a_n=a+(n-1)d\) \(\Rightarrow999=9+(n-1)d\) \(\Rightarrow9(n-1)=999-9=990\) \(\Rightarrow n-1=\frac{990}9=110\) \(\Rightarrow n=110+1=111\) Hence, there are total 111 numbers which are divisible by 9 in between 1 & 1000. Correct option is B) 111

How many numbers are divisible by 9 in between 1 and 1000 ? A) 100 B) 101 C) 110 D) 111

Answer»

Correct option is (D) 111

First number between 1 & 1000 which is divisible by 9 is 9

& last number between 1 & 1000 which is divisible by 9 is 999.

i.e., \(a_1=a=9\;\&\;a_n=999,d=9\)

\(a_n=a+(n-1)d\)

\(\Rightarrow999=9+(n-1)d\)

\(\Rightarrow9(n-1)=999-9=990\)

\(\Rightarrow n-1=\frac{990}9=110\)

\(\Rightarrow n=110+1=111\)

Hence, there are total 111 numbers which are divisible by 9 in between 1 & 1000.

Correct option is B) 111