Question

Question # 11
The age of a tree is 1/50th of the square of the owner's age. If the sum of their ages is 100, what is the age of the
owner?​

Answer 1

$\underline{\underline{\huge{\gray{\tt{\textbf Answer :-}}}}}$

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$\sf\large\bold{\orange{\underline{\blue{ Given :-}}}}$

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• The age of a tree is 1/50th of the square of the owner's age

• Sum of their ages is 100

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$\sf\large\bold{\orange{\underline{\blue{ To \: Find :-}}}}$

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• Age of the owner

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$\sf\large\bold{\orange{\underline{\blue{ Solution :-}}}}$

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Let the owner's age be "a"

Let the tree's age be "b"

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$\underline{\bold{\texttt{Square of owner's age :}}}$

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➜ a²

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$\underline{\bold{\texttt{1/50th of the square of owner's age :}}}$

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➜ $\sf \dfrac { 1 } { 50 } \times a ^2$

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Given that , The age of a tree is 1/50th of the square of the owner's age

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So,

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➜ $\sf b = \dfrac { 1 } { 50 } \times a ^2$ ⚊⚊⚊⚊ ⓵

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Also given that ,Sum of their ages is 100

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So ,

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➜ a + b = 100 ⚊⚊⚊⚊ ⓶

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⟮ Putting the value of "b" from ⓵ to ⓶ ⟯

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➜ a + b = 100

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➜ $\sf a + \dfrac { 1 } { 50 } \times a ^2 = 100$

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➜ $\sf \dfrac { 50a + a ^2 } { 50 } = 100$

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➜ 50a + a² = 5000

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➜ a² + 50a - 5000 = 0

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➜ a² + 100a - 50a - 5000 = 0

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➜ a(a + 100) -50(a + 100) = 0

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➜ (a + 100)(a - 50) = 0

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• a = - 100
• a = 50

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As age can't be negative

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Thus ,

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➨ a = 50

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• Hence the age of the owner is 50