Question

The tens digit in a 2-digit number is one more than the units digit, The difference between this number and the reversed number is 1/5 of the reversed number. what is the number

Answer 1

unit digit --- x
tens digit --- x+1

actual number = 10(x+1) + x = 11x + 10
number reversed = 10x + (x+1) = 11x + 1

11x + 10 - (11x + 1) = (1/5)(11x + 1)
9 = (1/5)(11x + 1)
45 = 11x + 1
x = 4

so the number is 54

check:
number: 54
reversed # : 45
difference between them = 54 - 45 = 9
1/5 of reverse # = (1/5)(45) = 9
looks good

Answer 2

number = t u = 10 t + u
10 t + u - 10 u - t = (1/5) (10 u + t)
(9 t - 9 u )5 = 10 u + t
45 t - 45 u = 10 u + t
55 u = 44 t
t = (55/44) u = (11 * 5 / 11*4) = (5/4) u
well either 54 or 45

try 54
54 - 45 = (1/5) (45) ?
Whew !