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Answer:
The original nimber is 67.
Step-by-step explanation:
Let the two digits be x and y.
According to the question.
The sum of two digits of a two digit number is
x + y = 13
or, x = 13 - y
And, a two digit number can be written as
x × 10 + y
when the digits are reversed, the number can be written as
y × 10 + x
the original number increases by 9. i.e.
y x 10 + x = x × 10 + y + 9
Replacing value of x by 13 - y,
y × 10 + 13 - y = 10(13 - y) + y + 9
10y + 13 - y = 130 - 10y + y + 9
9y + 13 = 139 - 9y
18y = 139 - 13
18y = 126
y = 126/18
y = 7
So, x = 13 - y
= 13 - 7
= 6
The original number is x × 10 + y = 6 x 10 + 7 = 67.