12 years ago, the ratio of the ages of Ram and Laxman was 2:1. After 13 years from now, the ratio of their ages will be 9:7. The sum of their present ages is:

Let the ages of Ram and Laxman 12 years ago be 2x and 1x, respectively.
Therefore, their present ages are:

Present age of Ram=2x+12
Present age of Laxman=x+12
After 13 years from now, their ages will be:

Age of Ram=(2x+12)+13=2x+25
Age of Laxman=(x+12)+13=x+25
According to the question, the ratio after 13 years is 9:7:

x+25
2x+25
​
=
7
9
​

Cross-multiplying to solve for x:

7(2x+25)=9(x+25)
14x+175=9x+225
14x−9x=225−175
5x=50
x=10
Now, find their present ages:

Present age of Ram=2(10)+12=32 years
Present age of Laxman=1(10)+12=22 years
The sum of their present ages is:

32+22=54 years