Question

Raj age after 6 year will be three seventh of this father age 10 year ago the ratio of their age was 1:5 Raj father age at Present

Answer 1

$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

$\:\:$

$\large{\green{\underline \bold{\tt{Given :-}}}}$

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• Raj age after 6 year will be three seventh of his father's age

$\:\:$

• 10 year ago the ratio of their age was 1:5

$\:\:$

$\large{\red{\underline \bold{\tt{To \: Find :-}}}}$

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• Their present ages

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$\large{\orange{\underline{\tt{Solution :-}}}}$

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• Let the present age of Raj be "R"

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• Let the present age of Father be "F"

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$\underline{\bold{\texttt{Raj's age after 6 years :}}}$

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➠ R + 6

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$\underline{\bold{\texttt{Father's age after 6 years :}}}$

$\:\:$

➠ F + 6

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$\purple{\underline \bold{According \: to \: the \ question :}}$

$\:\:$

Raj age after 6 year will be three seventh of his father's age

$\:\:$

➜ $\sf R + 6 = \dfrac { 3 } { 7 } \times (F + 6)$

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➜ 7(R + 6) = 3(F + 6)

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➜ 7R + 42 = 3F + 18

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➜ 3F - 7R = 42 - 18

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➜ 3F - 7R = 24 -------- (1)

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

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➠ R - 10

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

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➠ F - 10

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Also given that , 10 year ago the ratio of their age was 1:5

$\:\:$

So,

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➠ R - 10 : F - 10 = 1 : 5

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Or ,

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$\sf \dfrac { R - 10 } { F - 10 } = \dfrac { 1 } { 5 }$

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➜ F - 10 = 5R - 50

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➜ F - 5R = - 50 + 10

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➜ F - 5R = -40 ------- (2)

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⟮ Multiplying equation (2) by 3 ⟯

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We get,

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➜ 3F - 15R = -120 ------- (3)

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⟮ Subtracting equation (3) from (1) ⟯

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➜ 3F - 7R - (3F - 15R) = 24 - (-120)

$\:\:$

➜ 3F - 7R - 3F + 15R = 24 + 120

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➜ 8R = 144

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➜ $\sf R = \dfrac { 144 } { 8 }$

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➨ R = 18

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• Hence present age of Raj is 18 years

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⟮ Putting R = 18 in (2) ⟯

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➜ F - 5R = -40

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➜ F - 5(18) = -40

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➜ F - 90 = - 40

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➜ F = -40 + 90

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➨ F = 50

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• Hence present age of father is 50 years

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∴ The present ages of Father and Raj are 50 years & 18 years respectively

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Answer 2

$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

$\:\:$

$\large{\green{\underline \bold{\tt{Given :-}}}}$

$\:\:$

• Raj age after 6 year will be three seventh of his father's age

$\:\:$

• 10 year ago the ratio of their age was 1:5

$\:\:$

$\large{\red{\underline \bold{\tt{To \: Find :-}}}}$

$\:\:$

• Their present ages

$\:\:$

$\large{\orange{\underline{\tt{Solution :-}}}}$

$\:\:$

• Let the present age of Raj be "R"

$\:\:$

• Let the present age of Father be "F"

$\:\:$

$\underline{\bold{\texttt{Raj's age after 6 years :}}}$

$\:\:$

➠ R + 6

$\:\:$

$\underline{\bold{\texttt{Father's age after 6 years :}}}$

$\:\:$

➠ F + 6

$\:\:$

$\purple{\underline \bold{According \: to \: the \ question :}}$

$\:\:$

Raj age after 6 year will be three seventh of his father's age

$\:\:$

➜ $\sf R + 6 = \dfrac { 3 } { 7 } \times (F + 6)$

$\:\:$

➜ 7(R + 6) = 3(F + 6)

$\:\:$

➜ 7R + 42 = 3F + 18

$\:\:$

➜ 3F - 7R = 42 - 18

$\:\:$

➜ 3F - 7R = 24 -------- (1)

$\:\:$

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

$\:\:$

➠ R - 10

$\:\:$

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

$\:\:$

➠ F - 10

$\:\:$

Also given that , 10 year ago the ratio of their age was 1:5

$\:\:$

So,

$\:\:$

➠ R - 10 : F - 10 = 1 : 5

$\:\:$

Or ,

$\:\:$

$\sf \dfrac { R - 10 } { F - 10 } = \dfrac { 1 } { 5 }$

$\:\:$

➜ F - 10 = 5R - 50

$\:\:$

➜ F - 5R = - 50 + 10

$\:\:$

➜ F - 5R = -40 ------- (2)

$\:\:$

⟮ Multiplying equation (2) by 3 ⟯

$\:\:$

We get,

$\:\:$

➜ 3F - 15R = -120 ------- (3)

$\:\:$

⟮ Subtracting equation (3) from (1) ⟯

$\:\:$

➜ 3F - 7R - (3F - 15R) = 24 - (-120)

$\:\:$

➜ 3F - 7R - 3F + 15R = 24 + 120

$\:\:$

➜ 8R = 144

$\:\:$

➜ $\sf R = \dfrac { 144 } { 8 }$

$\:\:$

➨ R = 18

$\:\:$

Hence present age of Raj is 18 years

$\:\:$

⟮ Putting R = 18 in (2) ⟯

$\:\:$

➜ F - 5R = -40

$\:\:$

➜ F - 5(18) = -40

$\:\:$

➜ F - 90 = - 40

$\:\:$

➜ F = -40 + 90

$\:\:$

➨ F = 50

$\:\:$

• Hence present age of father is 50 years

$\:\:$

• ∴ The present ages of Father and Raj are 50 years & 18 years respectively

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