Question : 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?
Option 1: 1 : 1
Option 2: 1 : 2
Option 3: 3 : 5
Option 4: 4 : 5
Correct Answer: 3 : 5
Solution :
Let the initial number of parrots and pigeons on the tree are $7x$ and $9x$, respectively.
After an hour, 8 parrots fly away and 6 pigeons come and sit on the tree.
The number of parrots and pigeons on the tree now is $(7x - 8)$ and $(9x + 6)$, respectively.
According to the problem, the ratio of the parrots and the pigeons on the tree now is 1 : 4.
$⇒(7x - 8) : (9x + 6) = 1 : 4$
$⇒4(7x - 8) = 1(9x + 6)$
$⇒28x - 32 = 9x + 6$
$⇒19x = 38$
$⇒x = 2$
Substituting $x = 2$ in $7x - 8$, we get the number of parrots on the tree now as 6.
The number of sparrows that came and sat on the tree is 10.
Therefore, the ratio of the parrots and the sparrows that are now on the tree is 6 : 10 = 3 : 5.
Hence, the correct answer is 3 : 5.
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