Five times the sum of the digits of a two-digit number is 13 less than the original number. If you reverse the digits in the two-digit number, four times the sum of its two digits is 21 less than the reversed two-digit number.
The difference of the original two-digit number and the number with reversed digits is

Question

Five times the sum of the digits of a two-digit number is 13 less than the original number. If you reverse the digits in the two-digit number, four times the sum of its two digits is 21 less than the reversed two-digit number.
The difference of the original two-digit number and the number with reversed digits is

shinalcantara · Answer

Let 'x' be the number in the tens place
      'y' be the number in the units place
Then the original number would be x(10) + y
10x + y  ----original two-digit number
10y + x  ----reversed two-digit number
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Five times the sum of the digits of a two-digit number is 13 less than the original number
5(x+y) = (10x + y) - 13
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Distribute 5 to the quantity (x+y) and remove parenthesis
5x + 5y = 10x + y - 13
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Transpose 10x and y to the left side of the equation 
5x - 10x + 5y - y = -13
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Combine like terms
-5x + 4y = -13    ------equation 1
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If you reverse the digits in the two-digit number, four times the sum of its two digits is 21 less than the reversed two-digit number
4(x+y) = 10y + x -21
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Distribute 4 to the quantity (x+y) and remove parenthesis
4x + 4y = 10y + x - 21
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Transpose 10y and x to the left side of the equation 
4x - x + 4y - 10y = -21
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Combine like terms
3x - 6y = -21    ------equation 2
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Multiply equation 1 with 3 and equation 2 with 5
(-5x + 4y = -13)  x3     
-15x + 12y = -39   ------equation 1'
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(3x - 6y = -21)   x5
15x - 30y = -105    -----equation 2'
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Add equation 1' and equation 2'
    -15x + 12y = -39
+    15x - 30y = -105
               -18y = -144
                     y = 8
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Substitute y=8 to equation 1
-5x + 4y = -13
-5x + 4(8) = -13
-5x + 32 = -13
Transpose 32 to the right side
-5x = -13 - 32
-5x = -45
    x = 9
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10x + y   -----original number
10y + x   -----reversed number
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The difference would be
    10x + y - (10y + x)   = [10(9) + 8] -[10(8)+ 9]
                                      = 98 - 89
                                      = 9
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Therefore the difference between the original and the reversed is 9.