Question 482623
Let the tens digit be T, and the units digit U


As sum of digits = 15, then T + U = 15


The value of this number is: 10(T) + U. or 10T + U, and when reversed, we have: 10(U) + T, or 10U + T


Since the # formed by reversing the digits is 27 less than the original number, then we can say that:


10U + T = 10T + U – 27 -------->  – 9T + 9U = -27


We now have the following simultaneous equations:

    T +   U = 15 _____ (i) 
– 9T + 9U = - 27 _____ (ii)
9T + 9U = 135 _______ (iii) ----- Multiplying eq (i) by 9
18U = 108 _______ Adding eq (ii) and eq (iii)


U, or the units digit = {{{108/18}}}, or {{{highlight(6)}}}


Substituting 6 for U in eq (i), we get: T + 6 = 15 ----- T, or the tens digit = {{{highlight(9)}}}


Now, since the tens digit is 9, and the units digit is 6, this makes the number: {{{highlight_green(96)}}}


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When 96 (original #) is reversed, it becomes 69. 69 is in fact 27 less than 96 (96 - 69 = 27).


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