The sum of the digits of a 2-digit number is 9. When the digits are reversed, it is found that the resulting number is greater than the original number by 27. Find the number. s answer fast
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Answer:
Let the digits be x and y.
Then, x+y = 9
the original number is 10x+y.
On reversing, we get the new number as 10y+x
The new number is greater than the old number by 27, i.e.
(10y+x) - (10x+y) = 27
or 9y-9x = 27, or y-x = 3
and x+y = 9
Adding the two equations, we get 2y = 12 or y = 6.
Thus, x = 3.
Therefore, the original number is 36.
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Let the digit in ones place be x and the digit in tens place be 9-x.
Orginal number = 10(9-x)+x = 90-9x
New number = 10x+9-x = 9x+9
(9x+9)-(90x-9) = 27
9x+9-90x+9x = 27
18x-81 = 27
18x = 108
x = 6
Original number = 36
New number = 63
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