Question:
The sum of the digits of a two digit number is nine .also nine times this number is twice the number obtained by reversing the order of digits .find the number
Answer:
Let the digit in the number is xy
So, the number = 10x + y
Given
the sum of the digits of a two-digit number is 9
=> x+ y = 9 ..........................1
Again
9(10x + y) = 2(10y + x)
=> 90x + 9y = 20y + 2x
=> 90x + 9y - 20y - 2x = 0
=> 88x - 11y = 0
=> 88x = 11y
=> y = 88x/11
=> y = 8x .........2
Put value of y in equation 1, we get
8x + x = 9
=> 9x = 9
=> x = 9/9
=> x = 1
From equation 2, we get
y = 8*1
=> y = 8
So, the number = xy = 18
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