Math, asked by manish6574jha, 6 hours ago

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

Answered by shauryaprataps51
8

Answer:

8 is the answer bro enjoy

Answered by RvChaudharY50
5

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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