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Hey,
Lets talk about the original number first.
Let the unit digit be y and tens digit be x
=> Original number = 10x + y
Since sum of digits is 9,
=> x+y = 9 --------(1)
When we interchange the digit, the number formed will be,
10y + x
When we interchange the digits, the number formed is 27 greater than original number.
=> (10y + x) = (10x + y) + 27
=> 10y + x - x - y = 27
=> 9y - 9x = 27
=> y - x = 3 -----------(2)
Adding equation 1 and 2,
x + y + y - x = 9 + 3
=> 2y = 12
=> y = 6
Since,
x + y = 9
=> x + 6 = 9
=> x = 3
So,
x=3 & y=6
=> Original two digit number is 10x + y
=> Original number = 10×3 + 6
=> Original number = 36
Hope it Helped ;)
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