Question

sum of the digit of a two digit number is 11 the given number is less than the number obtained by interchanging the digit by 9 find the number​

Answer 1

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Answer 2

Answer :-

Number is 56.

Explanation :-

Let the digit at tens place be x and the digit at units place be y

Sum of digits = 11

⇒ x + y = 11 ---eq(1)

Number formed i.e Given number = 10x + y

Number formed when digits are interchanged = 10y + x

Given

Given Number = less than the Number formed when digits are interchanged

⇒ 10x + y = (10y + x) - 9

⇒ 10x + y - 10y - x = - 9

⇒ 9x - 9y = - 9

⇒ 9(x - y) = - 9

⇒ x - y = - 9/9

⇒ x - y = - 1 --eq(2)

Adding eq(1) and eq(2)

⇒ x + y + (x - y) = 11 + (-1)

⇒ x + y + x - y = 11 - 1

⇒ 2x = 10

⇒ x = 10/2

⇒ x = 5

Substitute x = 5 in x + y = 11

⇒ 5 + y = 11

⇒ y = 11 - 5

⇒ y = 6

Given number = 10x + y = 10(5) + 6 = 50 + 6 = 56

∴ the number is 56.