Question

13. The ratio of ten’s digit to the unit's digit of a two-
digit number is 2:3. If 27 is added to the number, the
digits interchange their places. Find the number.​

Answer 1

Let the ten's place digit be 'x'

and the one's place digit be 'y'

Therefore,the number=10x+y

and the intetchanged number=10y+x

Now,ratio=2:3

or,x:y=2:3

or,x/y=2/3

or,x=2y/3 --------(1)

Now,According to question,

10x+y+27=10y+x

or,10x-x+y-10y=-27

or,9x-9y=-27

or,9(x-y)=-27

or,x-y=-3

or,2y/3-y=-3(from(1))

or,(2y-3y)/3=-3

or,-y=-9

or,y=9

Now, in (1)

x=2y/3

=(2×9)/3

=18/3

=6

Therefore, the number is 69.(ANS)