Answer:
The Original number is 52
Explanation:
Let the two digits be x and y
The , The sum of the two Digits is 7
So
x +y = 7
x = 7-y-------------------------------(1)
The original number is [tex]x \times 10 +y[/tex]---------------(2)
Now if we interchange the digits
The interchanged number will be [tex]y \times 10 + x[/tex]---------(3)
Interchanged = Original – 27
[tex]y \times 10 + x = x \times 10 + y -27[/tex]
[tex]10y + x =10x + y -27[/tex]
Group the like terms
[tex]10y -y =10x -x -27[/tex]
[tex]9y = 9x -27[/tex]--------------------------(4)
Substituting (1) in(4)
[tex]9y = 9(7-y) -27[/tex]
[tex]9y = 63 -9y -27[/tex]
[tex]9y+9y = 63-27[/tex]
[tex]18 y = 36[/tex]
[tex]y =\frac{36}{18}[/tex]
y = 2-------------------------------------(5)
Substituting (5) in(1)
x = 7 -y
x =7-2
x =5
Now From eq(1)
The original number will be
=10x +y
= 10(5) +2
= 50 +2
=52
