Question

A two digit number becomes five -sixth of itself when its digits are reversed .the two digits differ by one. what is the number??​

Answer 1

Let the 2 digits of a two digit number be x and y.

Then the two digit no so formed will be (10x+y) where x is at 10's place and y is at unit place.

By question, (5/6)×(10x+y)=(10y+x).......(1)

Also, (x-y)=1.......(2)

From (2), x =(y+1)

From (1),

5(10x+y)=6(10y+x)

Or, 50x+5y=60y+6x

Or, 44x=55y

Or,44(y+1)=55y

Or,44=11y

Therefore y=4.

Then,X=(y+1)=4+1=5.

Hence the required no is (10x+y)=(10*5+4)=54.