Find the number of such number
of multiples of 9 less than 2012 and having sum of the digits as 18.
Answers
The number of multiples of 9 less than 2012 and having sum of digits as 18 is 118.
We have the multiples of 9.
The last multiple of 9 less than 2012 is 2007.
Also digits should add up to 18.
For 2 digit number,
- only 99 adds up to 18.
For 3 digit numbers ,
- Starting with 1 : 198 and 189 add up to 18 : 2 nos.
- Starting with 2 : 297, 288, 297 ad up to 18 : 3nos.
- Similarly,
- 3 : 4 nos.
- 4 : 5 nos.
- 5 : 6 nos.
- 6 : 7 nos.
- 7 : 8 nos.
- 8 : 9 nos.
- 9 : 10 nos.
- Total = 1 + 2+ 3+ ... 10 = 55
For 4 digit number only 1000s are possible.
Second digit starting with ,
- 0 : 1098 , 1098 =2 nos.
- 1 : 3 nos
- 2 : 4 nos.
- 3 : 5 nos
- 4 : 6 nos
- 5 : 7 nos
- 6 : 8 nos
- 7 : 9 nos
- 8 = 10 nos
- 9 = 9 nos
Therefore,
total = 2 + 3 + 4 + ...10 + 9 = 55 -1 + 9 = 63.
Therefore total number of multiples less than 2012 and having sum of digits as 18 is 118.
Answer:
109
Step-by-step explanation:
2 digit number:- 99 :-1 number
3digit number:-
189, 198 :-2 numbers
279,297,288:-3 numbers
369, 396, 387, 378:-4 numbers
similarly, 477:- 5 numbers
567:-6numbers
666:- 7 numbers
765.:- 8
So, 1+2+3+4+5+6+7+8+9+10=55numbers
4digit numbers:-
1098, 1089= 2 numbers
1179, 1197= 2 numbers
1269, 1296 , 1287, 1278 = 4 numbers
1359, 1395= 5 numbers
So, 2+2+4+5+6+7+8+9+10= 54 numbers
Total numbers:- 55+54= 109