Question

sum of digits of a number is 8 but when 5 is added.. digits of the number is equal. find the number .. full process

Answer 1

Let the given number be xy.  Let the number we get after adding 5 be zz.

So :  10 x + y + 5 = 10 z + z = 11 z

Since adding 5 to units digit y, causes units digit z and a carry to tens digit :  y+5 = 10+z

Adding a carry to tens digit results in new tens digit z :        x+1 = z

Solving these equations :      y = z + 5 = x + 6

Let x = 0, 1, 2, 3.     The answers are :   06   or  17  or 28  or  39.

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3 digit numbers.

Let the number be   xyz.

100x + 10y + z + 5 = 100 w + 10 w + w = 111 w    ---(1)

Also:   z + 5 = 10 + w     =>  z = w + 5            ---- (2)

            y+1 = w           --- (3)

(1) becomes:   100 x + 10w -10 + w + 5  + 5 = 111 w    => 100 x = 100 w

          x = w.         y = w – 1 = x – 1.        z = x + 5

So the numbers are: 

  x=1,   106  ;   x = 2,  217;    x = 3,  328 ;    x = 4,  439

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4 digit numbers:     1106,   2217,   3328,   4439

5 digit numbers:     11106, 22217,  33328,  44439