Question

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

Answer 1

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Answer 2

Let the digits be x and y
When we have to write it in a way of two digit number we write it like
10x + y

Now reversing the digits we have
10y + x

Here given that 10x + y< 10y + x by 9

This means 10x + y + 9 = 10y + x
=> 10x + y -10y - x = -9
9x - 9y = -9
9(x-y) = -9
x - y = -9/9
x - y = -1

And we are given their sum as 11
That is x + y = 11
Adding x + y and x - y we have
x + y + x - y = 11 +(-1)
= 2x = 11-1
2x = 10
x = 10/2 = 5


Now substituting the value in first equation
x + y = 11
=> 5 + y = 11
y = 11 - 5
y = 6


So the number is
10x + y
= 50 + 6
= 56



56 is your answer.



Hope it helps dear friend ☺️✌️✌️