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in circle o is central point,PS is diameter, in triangle PQR ,OQM,SQT seg PR,OM,ST are parallel And PR,OM,ST are particular to QR and PR=9 cm ,PS=10cm ,find ST

in circle o is central point ,PS is diameter,in

Present age of two friends are in 3:5, five years later there age will be 7:11. Find present age.
In this question we will make sure the difference b/w first and second ratio must be same. Multiply first by 11-7=4 and second by 5-3=2.
we will obtain first ratio as 12:20 and second ratio as 14:22.
Now since age will have same difference through the condition, we can conclude that this 2 unit(which is difference b/w 12 and 14 or 20 and 22) is equal to 5 years. Therefore 12 unit is eqaul to 30 years and 20 unit is 50 years. It is present age.
Here I need to know the concept why after multiplying the initial ratios by each others difference make there difference equal. I mean why multiplying 3:5 with 4 and 7:11 with 2 make there difference equal.

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11=20
12=31
13=42
14=53
18=?