There are 2 trees in a garden tree A and tree B and in both

There are 2 trees in a garden: tree A and tree B, and in both trees are some birds. The birds of tree A say to the birds of tree B that if one of you comes to our tree then our population will be double your population. Then the birds of tree B tell the birds of tree A that if one of you comes here then our population will be equal to that of yours. How many birds are in each tree?

Solution

Let x be the number of birds on tree A and y be the number of birds on tree B initiaaly .

Now using the given condition it follows:

If 1 bird is removed from tree B then no. Of birds on tree B is y-1 and went to tree A then no. Of birds become x+1. Given x+1=2(y-1) => x-2y=-3 ........(i)

Now if 1 bird is removed from tree A and added to tree B then given that x-1=y+1=> x-y=2........ (ii)

Solving (i) and (ii) we get x=7 and y=5

As x=y+2 from (ii) . Putting this in (i) we get

y+2-2y = -3=> -y=-5 => y=5. And thus x=5+2=7