The tens digit is two less than the units digit. if the digits are reversed, the sum of the reversed number and the original number is 154. find the original number.

Let the number be xy then we have the following system of equations:-

y - x = 2(1)
10x+y + 10y + x = 154
11x + 11y = 154     Divide thru by 11:-

x + y = 14(2)

Add equation (1) AND (2):-

2y = 16

y = 8  
and x = 8-2 = 6

So your required number is 68.