The sum of the digits of a 2 digit number is 13. The number formed by interchanging the digits is 45 more than the original number. Find the original number.

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Solution

let the digits be X and Y
X+Y=13
X=13-Y
Let original number be 10X+Y
10Y+X=10X+Y+45

Replacing X with 13-Y
10Y+13-Y=130-10Y+Y+45

9Y+9Y=130-13+45
18Y=162
Therefore
Y=9
X=13-Y=13-9=4

Therefore
Original number is 10X+Y
=40+9
=49

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The sum of the digits of a 2 digit number is 13. The number formed by interchanging the digits is 45 more than the original number. Find the original number.

let the digits be X and Y X+Y=13 X=13-Y Let original number be 10X+Y 10Y+X=10X+Y+45 Replacing X with 13-Y 10Y+13-Y=130-10Y+Y+45 9Y+9Y=130-13+45 18Y=162 Therefore Y=9 X=13-Y=13-9=4 Therefore Original number is 10X+Y =40+9 =49

let the digits be X and Y
X+Y=13
X=13-Y
Let original number be 10X+Y
10Y+X=10X+Y+45

Replacing X with 13-Y
10Y+13-Y=130-10Y+Y+45

9Y+9Y=130-13+45
18Y=162
Therefore
Y=9
X=13-Y=13-9=4

Therefore
Original number is 10X+Y
=40+9
=49