Let the original number be ¯¯¯¯¯¯yx; i.e., 10y+x. We know x+y=7. The number obtained by reversing the digits in ¯¯¯¯¯¯xy, i.e., 10x+y. The second condition gives 10x+y−2=2(10y+x). Thus we have two equations:
x+y=7....(1)
8x−19y=2....(2)
Multiply the equation (1) by 19 and get
19x+19y=133.
Adding this to (2), we obtain 27x=135. This gives x=5. Hence y=7−x=7−5=2.
The required number is 25.