Question

ten year ago , the father was six times as old as his daughter .After 10 years,he will be twice as old as his daughter .find thier present ages.​

Answer 1

A n s w e r

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G i v e n

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• Ten year ago , the father was six times as old as his daughter

• After 10 years,he will be twice as old as his daughter

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F i n d

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• Their present ages

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S o l u t i o n

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Let the present age of the father be "a"

Let the present age of his daughter be "b"

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$\underline{\bold{\texttt{Father's age 10 years ago :}}}$

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➠ a - 10

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$\underline{\bold{\texttt{Daughter's age 10 years ago :}}}$

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➠ b - 10

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Given that , Ten year ago , the father was six times as old as his daughter

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➜ (a - 10) = 6(b - 10)

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➜ a - 10 = 6b - 60

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➜ a - 6b = -50 ⚊⚊⚊⚊ ⓵

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$\underline{\bold{\texttt{Father's age 10 years later :}}}$

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➠ a + 10

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$\underline{\bold{\texttt{Daughter's age 10 years later :}}}$

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➠ b + 10

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Given that , After 10 years,he will be twice as old as his daughter

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➜ (a + 10) = 2(b + 10)

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➜ a + 10 = 2b + 20

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➜ a - 2b = 10 ⚊⚊⚊⚊ ⓶

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⟮ Equation ⓶ - ⓷ ⟯

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➜ a - 2b -(a - 6b) = 10 - (-50)

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➜ a - 2b - a + 6b = 10 + 50

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➜ 4b = 60

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➜ $\sf b = \dfrac { 60 } { 4 }$

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➜ b = 15 ⚊⚊⚊⚊ ⓷

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• Hence daughter is 15 years old

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⟮ Putting b = 15 from ⓷ to ⓶ ⟯

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➜ a - 2b = 10

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➜ a - 2(15) = 10

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➜ a - 30 = 10

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➜ a = 10 + 30

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➨ a = 40

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• Hence the present age of father is 40 years