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
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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.