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the sum of digits of a tow digit number is 13.if the number is subtracted from the number obtained by interchanging the digit the result is 45.what is the number ?
Let the ten's place digit be x and one's place digit be y

according to question x + y = 13.
original number 10x + y 
reversed number 10y + x

10y + x - (10x + y) = 45 
10y + x - 10x - y = 45 
-9x + 9y = 45
Now
(x + y = 13) * 9
= 9x + 9y = 117
(-9x + 9y = 45) + ( 9x + 9y = 117)
18y = 162
y = 9
x + y = 13
x + 9 = 13
 x = 13 -9 = 4
Original number is 10x + y = 10 * 4 + 9
= 49