Question

a number consisting of two digits becomes 5/6 of itself if its digits are interchanged . if the the difference of the digits is 1, find the number.

Answer 1

let the two digit be x and y (x at ten's place and y at one's place)
so as per ques
x-y = 1 
and the original number is 10x +y
so on interchaning the digits
10y +x = 5(10x + y)/6
=>60y+6x = 50x+5y
=> 55y = 44x

since x-y = 1 => x = 1+y

so 55y = 44x
55y =  44(1+y)
55y = 44+44y

55y-44y = 44
=> y = 4 and x = 5
so original umber is
54

Answer 2

If you want a more formal approach:

The number is two digits so: it can be seen as10x+y10x+y

Where x is the first digit (10s) and y the second.

Now we have two equations with two variables: 5/6(10x+y)=10y+x5/6(10x+y)=10y+x

50x+5y=60y + 6x

44x= 55y

Y=4/5x

Also we have

|x−y|=1|x−y|=1

Thus

X/5=1

X=5 and y=4

We get that the number is 54