On a tree, there are some parrots and some pigeons in the ratio of 7 : 9, respectively. After an hour, 8 parrots fly away, and 6 pigeons and 10 sparrows come and sit on the tree. The ratio of the parrots and the pigeons on the tree now is 1 : 4. What is the ratio of the parrots and the sparrows that are now on the tree?

On a tree, there are some parrots and some pigeons in the ratio of 7 : 9, respectively.

Let's assume the number of parrots and pigeons initially is 7y and 9y.

After an hour, 8 parrots fly away, and 6 pigeons and 10 sparrows come and sit on the tree.

Now number of parrots = (7y-8)

number of pigeons = (9y+6)

number of sparrows = 10

The ratio of the parrots and the pigeons on the tree now is 1 : 4.

$$\frac{(7y-8)}{(9y+6)}\ =\ \frac{1}{4}$$

Ratio of the parrots and the sparrows now on the tree = (7y-8) : 10

= $$(7\times2-8) : 10$$

= $$(14-8) : 10$$

= $$6 : 10$$

= 3 : 5