The ratio of the mango trees and orange trees is $7 : 9$ . If $5$ mango trees and $5$ orange trees were planted in addition the ratio would be $27 : 34$ . Find the number of mango trees.

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Solution

Let the number of mango trees and orange trees be $7 a$ and be $9 a$ .
If more $5$ tress of each type were planted, their numbers would be $7 a + 5 : 9 a + 5$
Given, the ratio of $7 a + 5 : 9 a + 5$ is equal to $27 : 34$
$\Rightarrow 7 a + 5 : 9 a + 5 = 27 : 34$
$\Rightarrow \frac{7 a + 5}{9 a + 5} = \frac{27}{34}$
Om cross multiplying, we have
$238 a + 170 = 243 a + 135$
$35 = 5 a$
$a = 7$
Let the number of mango trees and orange trees are $7 \times 7 = 49$ and be $9 \times 7 = 63$ respectively.

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The ratio of the mango trees and orange trees is 7:9. If 5 mango trees and 5 orange trees were planted in addition the ratio would be 27:34. Find the number of mango trees.

The ratio of the mango trees and orange trees is $7 : 9$ . If $5$ mango trees and $5$ orange trees were planted in addition the ratio would be $27 : 34$ . Find the number of mango trees.