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Question : The sum of the digits of a two - digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.
Solution :
Given,
The sum of the digits of a two digit number is 9.
let the two numbers be x and y
Then the number is 10x + y
The sum of the digits = 9
According to the problem,
x + y = 9 -------(1)
When the number is reversed = 10y + x
Then nine times this number is twice the number obtained by reversing the order of the digits.
9(10x + y ) = 2(10y + x )
90x + 9y = 20y + 2x
90x - 2x = 20y - 9y
88x = 11y
8x = y ----(2)
Subtitute y in eq - (1)
x + (8x) = 9
9x = 9
x = 1
substitute x in eq ---(2)
8(1) = y
y = 8
Therefore, the number = 10(1) + (8) = 18