Integers are listed from 700 to 1000. In how many integers is the sum of the digits 10? (a) 6 (b) 7 (c) 8 (d) 9
Answers
Answer:
8 is the answer bro enjoy
Solution :-
Let us assume that, the required three digits numbers are written as (100x + 10y + z) , where x = 7, 8 and 9 .
Taking x = 7 :-
→ x + y + z = 10
→ 7 + y + z = 10
→ y + z = 10 - 7
→ y + z = 3
then,
→ when y = 0, z = 3
→ when y = 1, z = 2
→ when y = 2, z = 1
→ when y = 3, z = 0
therefore, when x = 7, total 4 integers are possible .
Taking x = 8 :-
→ x + y + z = 10
→ 8 + y + z = 10
→ y + z = 10 - 8
→ y + z = 2
then,
→ when y = 0, z = 2
→ when y = 1, z = 1
→ when y = 2, z = 0
therefore, when x = 8, total 3 integers are possible .
Taking x = 9 :-
→ x + y + z = 10
→ 9 + y + z = 10
→ y + z = 10 - 9
→ y + z = 1
then,
→ when y = 0, z = 1
→ when y = 1, z = 0
therefore, when x = 9, total 2 integers are possible .
Hence, we can conclude that,
→ Integers with hundred's digits as 7 = 703, 712, 721, 730 = Total 4
→ Integers with hundred's digits as 8 = 802, 811, 820 = Total 3
→ Integers with hundred's digits as 9 = 901, 910 = Total 2 .
∴ Total (d) 9 integers are in the list .
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