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  4. A hybrid mango tree, whose life span is 10 years, starts giving fruits from the first year onwards. In the nth year it produces 11 n raw mangoes. But during the first half of the tree's life, every year, a certain number, which is constant, fail to ripen into fruits. During the second half of the tree's life, every year,the number of raw fruits that fail to ripen is half the corresponding number in the first half of the tree's life. In the fourth year of the tree's life, it produces 36 ripe mangoes. How many mangoes ripen during the 9th year of the tree's life?

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Q. A hybrid mango tree, whose life span is 10 years, starts giving fruits from the first year onwards. In the $n$th year it produces $11 n$ raw mangoes. But during the first half of the tree's life, every year, a certain number, which is constant, fail to ripen into fruits. During the second half of the tree's life, every year,the number of raw fruits that fail to ripen is half the corresponding number in the first half of the tree's life. In the fourth year of the tree's life, it produces 36 ripe mangoes. How many mangoes ripen during the 9th year of the tree's life?

Pair of Linear Equations in Two Variables

Solution:

Every year in the first half of the tree's life, the number of mangoes that cannot become ripen fruit is $\gamma$ (say).
The number of fruits produced in the $x$ th year $=$ $11 x-y$
Number of fruits produced in 4th year $=36$
$\Rightarrow 11(4)-\gamma=36 \Rightarrow \gamma=8$
Number of fruits produced in $x$ th year of the second half-life $=11 x-\frac{\gamma}{2}$
Number of fruits produced in the 9 th year $=11(9)-\frac{8}{2}=99-4=95$