The digits of which two digit number are reversed when 27 is added to it.

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

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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