The ratio of the tens digit to the ones digit of a 2-digit number is 2:3. If 27 is added to the number, the digits interchange their places. Find the number.
Let the ones digit and tens digit of the number be a,b respectively.
number =ba
given that,
ba=23
→3b=2a→b=2a3 -------(1)
it is also given that,
ba+27=ab
(10b+a)+27=10a+b
9a−9b=27
9(a−b)=27
a−b=3
put the value of b from equation 1
a−2a3=3
3a−2a=9
a=9,b=2×93=6
number =69