From the given information, the original number is 180. 02
Let the unit digit be x
The unit in tens is x+ 5
The original number = 10(x+5) + x = 11x + 50
The reversed number = 10x+ (x+5) = 11x+5
From the information given, we have that
(11x + 50) - (11x + 5) = 1/4 (11x + 50)
Expand the expression
11x + 50 - 11x - 5 = 1/ 4(11x + 50)
Collect like terms
11x - 11x + 50 - 5 = 1/ 4 (11x + 50)
45 = [tex]\frac{11x + 50}{4}[/tex]
Cross multiply
45 * 4 = 11x + 50
180 = 11x + 50
11x = 180 -50
11x = 130
x = 130/11
x = 11. 82
To find the original number, we have
Original number = 11x + 50
Substitute the value of x
Original number = 11(11.82) + 50
Original number = 130. 02 + 50
Original number = 180. 02
Therefore, the original number is 180. 02
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