The digits of which two digit number are reversed when 27 is added to it.
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Let the digits of the number we need to find be ab. So the number is 10*a + b. The digits are reversed when 27 is added to it.
We can use this to create the equation: 10*a + b + 27 = a + 10*b
=> 9*a - 9*b = -27
=> b - a = 3
So we have b as 1, 2, 3, 4, 5 or 6 and a is 4, 5, 6, 7, 8 or 9
Therefore for all the numbers 14 , 25 , 36 , 47 , 58 and 69 the digits are reversed when 27 is added.
The required numbers are 14 , 25 , 36 , 47 , 58 and 69
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Let x be in 10th place and y in units place.
Then the value of the number = 10x+y.
Let us add 27 to 10x+y.: 10+y+27 which is the revwesed number 10y+x by data.
=> 10x+y+27 = 10y +x.
So 27 = 10y +x - 10x-y = 9(y-x).
So 27 = 9(y-x).
Oy y-x = 27/9 = 3.
Therefore y = x+3.
So the possible solutions are 14 or 25 or 36 or47 or 58 or 69.
Tally:
14+27 = 41
25+27 = 52
36+27 = 63
47+27 = 74
58+27 = 85
69+27 = 96.
Solutions are 14 , 25, 36, 47, 58 and 69.
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