Solution to Never ask a womens age

2450 = 1 * 2 * 5 * 5 * 7 * 7

so list down all the possible sets ( x, y, z) such that xyz = 2450;
some sets are (1,49,50); (2,35,49); (5,10,49); (7,7,50) and so on.....

Now the bartender says that the sum of their ages is equal to your age. Since the person knows his own age but still cannot get the answer, this means that 'x + y + z ' is same for multiple sets say (x1,y1,z1) and (x2,y2,z2).....

only one such combination of multiple sets exists i.e
(5,10,49); (7,7,50) both of which sum up to 64.

Now we have to choose from one of these sets...

Now the bartender says that the oldest lady is older than peterson. Which means that the set must be (5,10,49).

So the ages must be 5,10,49