Question

The ratio of tens digit to the unit 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 tens digit
Let  = the units digit
------------------------
(1) 
(2) 
----------------------------
(2) 
(2) 
(2) 
----------------
(1) 
Substitute (1) into (2)
(2) 

(2) 
(2) 
and
(2) 
(2) 
(2) 
(2) 
The original number is 69
check:
(2) 
(2) 
(2) 
(2) 
OK