number of two digits = x
one-third of that number = 

successor of that number = x+1

one-fourth of successor of that number = 


One – third of a number of two digits is greater than one – fourth
of its successor by 1 . Find the number .

Replace the underlined words by 

 is greater than one – fourth of its successor by 1 . Find the number .

Replace the underlined words by 

 is greater than  by 1 . Find the number .

Mentally translate this by reasoning

If a first thing is greater than a second thing by ONE, that means that the
the first thing equals the second thing PLUS ONE.  So



Multiply through by 



4x = 3(x + 1) + 12
4x = 3x + 3 + 12
4x = 3x + 15
 x = 15

Turns out that they didn't need to tell us that it has two digits.

Checking:

One – third of 15, which is 5, is greater than one – fourth
of (15's) successor 16, (which is 4), by 1.  It's true that
5 is indeed greater than 4 by 1, so we have the correct 
answer, 15.

Edwin