Question

In a two digit number, the ratio of the digits at the unit's place and the ten's place is 3:2. If the digits are reversed, the resulting number is 27 more than the original number. Find the two digit number.

Answer 1

Let the units place be x and tens place be y.
Then, the two-digit number is 10y + x.
GIven, x : y = 3 : 2---(1)
If the digits are reversed,
The reversed number is 10x + y.
The original number is 10y + x.
Given the resulting number with reversed digits is 27 more than the original number.
⇒ 10x + y - 27 = 10y + x
⇒  9x - 9y - 27 = 0
⇒ x = y + 3---(2)
Using (2) in (1), gives:

${\displaystyle \frac{y+3}{y}=\frac{3}{2}}$

⇒ 2y + 6 = 3y
⇒ y = 6
Thus, x = y + 3 = 9
The number is 10y + x = 10 x 6 + 9 = 69.