Question 612620
the sum of a 2 digit number and number formed by reversing the digits is 88 if the digits differ by 2. find the no.


Let the tens digit be T, and the units digit, U
Then: 10T + U + 10U + T = 88


11T + 11U = 88
11(T + U) = 11(8)
T + U = 8
T = 8 - U

|T – U| = 2, since it’s not known which digit is larger


|8 – U – U| = 2 ----- Substituting 8 – U for T 


|8 – 2U| = 2


8 – 2U = 2   OR    8 – 2U = - 2 


– 2U = 2 – 8    OR     – 2U = - 10 


- 2U = - 6    OR    U = - 10/- 2


U = {{{(-6)/-2}}}   OR   U = {{{(- 10)/- 2}}}


U, or units digit = 3 or 5


This means that the original number could be either {{{highlight_green(53)}}} or {{{highlight_green(35)}}}


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