Question

Present age of a sun is one third of his father . 10 years from now , the son will be exactly half the age of his . What were the ages of father and his son 5 years back ?

Answer 1

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

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$\green{\underline \bold{Given :}}$

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• Present age of a son is one third of his father.

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• After 10 yrs son will be exactly half the age of father.

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$\red{\underline \bold{To \: Find:}}$

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• Ages of father and his son 5 years back.

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

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Let the present age of father be 'x'

Let the present age of son be 'y'

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

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Present age of a son is one third of his father.

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$\purple\longrightarrow$ $\sf y = \dfrac { 1 } { 3 } \times x$ ------(1)

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$\underline{\bold{\texttt{10 yrs later ages will be :}}}$

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• Father = x + 10

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• Son = y + 10

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Given that,

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10 years from now , the son will be exactly half the age of his father.

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So,

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$\sf \longmapsto \dfrac { (x + 10)} { 2 } = (y + 10)$ ----(2)

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$\underline{\bold{\texttt{Putting the value of y from (1) to (2)}}}$

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$\sf \longmapsto \dfrac { (x + 10) } { 2 } = \dfrac { x } { 3 } + 10$

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$\sf \longmapsto \dfrac { (x + 10) } { 2 } = \dfrac { x + 30 } { 3 }$

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$\sf \longmapsto 3x + 30 = 2x + 60$

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$\sf \longmapsto 3x - 2x = 60 - 30$

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$\bf \dashrightarrow x = 30$

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Hence father's present age is 30yrs

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Son's present age will be $\rm \dfrac { 30 } { 3 }$

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i.e 10yrs

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$\underline{\bold{\texttt{5 yrs ago ages were :}}}$

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• Father = 30 - 5

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• Son = 10 - 5

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Hence 5 yrs back father was 25 yrs old and son was 5 yrs old

$\rule{200}5$

Answer 2

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$\huge\bold{\mathtt{\underline{\underline{\purple{QUESTION}}}}}$

➡ Present age of a son is one third of his father . 10 years from now , the son will be exactly half the age of his . What were the ages of father and his son 5 years back ?

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$\huge\bold{\mathtt{\underline{\underline{\purple{ANSWER}}}}}$

$\bigstar\large\bold{\mathrm{\green{\underline{Given:}}}}$

☯ Present age of a sun is one third of his father.

☯ 10 years from now , the son will be exactly half the age of his .

$\bigstar\large\bold{\mathrm{\green{\underline{To\:find:}}}}$

☯ Ages of father and his son 5 years back .

$\bigstar\large\bold{\mathrm{\green{\underline{Solution:}}}}$

☯ Let the present age of son be x .

☯ And the age of father be y .

★ Now , According To The Question :

→ $\sf x\: =\: \dfrac{1}{3} \times y$

→ $\sf x\:=\: \dfrac{y}{3}$ ----- equation 1

✴ 10 years later age of -

⭐ Father = y + 10

⭐ Son = x + 10

★ Now , According To The Question :

→ $\sf \dfrac{y+10}{2} \:=\: x + 10$ ----- equation 2

⏩ Now , substitute value in equation 2 from equation 1 .

→ $\sf \dfrac{y+10}{2} \:=\: \dfrac{y}{3} + 10$

→ $\sf \dfrac{y+10}{2} \:=\: \dfrac{y+30}{3}$

→ $\sf 3y+30\:=\: 2y+60$

→ $\sf 3y-2y \:=\: 60-30$

→ $\sf y \:=\: 30$

$\large\bold{\boxed{\mathrm{\orange{y=30}}}}$

⭐ PRESENT AGE OF FATHER = 30 years

$\large\bold{\boxed{\mathrm{\orange{x= \dfrac{30}{3}\:=\:10}}}}$

⭐ PRESENT AGE OF SON = 10 years

✴ 5 years ago -

★ Age of Father = 30-5 = 25 years

★ Age of Son = 10-5 = 5 years

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