Question

the sum of the ages of son and father is 56 years. After four years the age of the father will be trice the sons age. find thier age's​

Answer 1

AnswEr :

¤ Let's say, that the father's present age be x years and son's present age be y years respectively.

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$\underline{\bigstar\:\textsf{According to the given Question :}}$

• Sum of the ages of son and father is 56 years.

$:\implies\sf \Big\{Father's\;age\Big\} + \Big\{Son's\;age\Big\} = 56 \\\\\\:\implies\sf x + y = 56\qquad\quad\dfrac{\quad}{}\:eq^{n}\;(1)$

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• Also, after four years the age of the father will be thrice the son's age.

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After four years,

• Father's age = (x + 4) years
• Son's age = (y + 4) years

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$\dashrightarrow\sf x + 4 = 3\Big\{y + 4\Big\} \\\\\\\dashrightarrow\sf x + 4 = 3y + 12 \\\\\\\dashrightarrow\sf x - 3y = 12 - 4 \\\\\\\dashrightarrow\sf x - 3y = 8 \\\\\\\dashrightarrow\sf x = 8 + 3y\qquad\quad\dfrac{\quad}{}\:eq^{n}\;(2)$

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$\underline{\bigstar\:\textsf{Putting the value of x in eq\;(1) :}}$

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$\twoheadrightarrow\sf x + y = 56 \\\\\\\twoheadrightarrow\sf 8 + 3y + y = 56 \\\\\\\twoheadrightarrow\sf 8 + 4y = 56 \\\\\\\twoheadrightarrow\sf 4y = 56 - 8 \\\\\\\twoheadrightarrow\sf 4y = 48 \\\\\\\twoheadrightarrow\sf y = \cancel\dfrac{48}{4} \\\\\\\twoheadrightarrow\underline{\boxed{\pmb{\frak{\purple{y = 12}}}}}\;\bigstar$

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Therefore,

• Present age of son, y = 12 years.
• Present age of father (x + 12 = 56), x = 44 years.

$\therefore{\underline{\textsf{Hence, present age of father \& his son is \textbf{44 years} \sf{and} \textbf{12 years}.}}}$

Answer 2

Given that , The sum of the ages of son and father is 56 years & After four years the age of the father will be thrice the sons age .

Exigency To Find : Their [ Father and son ] present ages ?

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❍ Let's say the Present age of Father be x yrs .

⠀⠀⠀Given that ,

⠀⠀⠀⠀⠀⠀▪︎⠀The sum of the ages of son and father is 56 years .

$\qquad \therefore \sf Age_{(Father)} \:+ \: Age_{(Son)} \: = \:56 \:years \:\\\\\qquad:\implies \sf Age_{(Father)} \:+ \: Age_{(Son)} \: = \:56 \:years \:\\\\\qquad:\implies \sf x \:+ \: Age_{(Son)} \: = \:56 \: \:\\\\\qquad:\implies \sf \: Age_{(Son)} \: = \:(\:56 - x \:) \: \:\\\\\qquad :\implies \underline {\boxed {\purple{\pmb{\frak{\: Age_{(Son)} \: = \:(\:56 - x \:) \: years\: }}}}}$

⠀⠀⠀⠀⠀⠀☆ After 4 years their ages :

• The age of Father will be : ( x + 4 ) yrs .
• The age of Son will be : ( 56 - x + 4 ) yrs

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$\qquad \underline {\purple {\bf{ \bigstar \: According \:to \:the \:Question \::\;}}}$

⠀⠀⠀⠀⠀━━━ After four years the age of the father will be thrice the sons age.

$\qquad \dashrightarrow \sf 3 \bigg\lgroup \sf{ Son \: Age \:_{(\:After \:4 \:yrs\:)} }\bigg\rgroup =\bigg\lgroup \sf{ Father's \: Age \:_{(\:After \:4 \:yrs\:)} }\bigg\rgroup \\\\\qquad \dashrightarrow \sf 3 \bigg\lgroup \sf{ 56 - x + 4 }\bigg\rgroup =\bigg\lgroup \sf{ x + 4 \: }\bigg\rgroup \\\\\qquad \dashrightarrow \sf \bigg\lgroup \sf{ 168 - 3x + 12 }\bigg\rgroup =\bigg\lgroup \sf{ x + 4 \: }\bigg\rgroup \\\\\qquad \dashrightarrow \sf 168 - 3x + 12 = x + 4 \: \\\\\qquad \dashrightarrow \sf 168 + 12 - 4 = x + 3x \: \\\\\qquad \dashrightarrow \sf 180 - 4 = x + 3x \: \\\\\qquad \dashrightarrow \sf 4x = 176 \: \\\\\qquad \dashrightarrow \sf x = \cancel {\dfrac{176}{4}} \: \\\\\qquad \dashrightarrow \sf x = 44 \: \\\\\qquad \dashrightarrow \underline {\boxed {\purple{\pmb{\frak{\: x\: ( or \: Age\:of \:Father\:) \: = \:44 \: years\: }}}}}$

Therefore,

• Present age of Father is x = 44 yrs
• Present age of Son is ( 56 - x ) = ( 56 - 44 ) = 12 yrs .

$\qquad \therefore \underline {\sf \: Hence , \: The \:Present \:ages \:of \:father \: and \:son \:are \:\pmb{\bf 44 \: yrs \: \& \: 12 \:yrs \:}\:, respectively \:}$

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$\qquad \qquad \underline {\mathbb{ \pink{\bigstar \: V\:E\:R\:I\:F\:I\:C\:A\:T\:I\:O\:N\:\: \::}}}$

⠀⠀⠀⠀⠀Given that ,

⠀⠀⠀⠀⠀━━━ After four years the age of the father will be thrice the sons age.

$\dashrightarrow \sf 3 \bigg\lgroup \sf{ Son \: Present\:Age \:+ \:4 }\bigg\rgroup =\bigg\lgroup \sf{ Father's \:Present \: Age \:+ \:4 }\bigg\rgroup \\\\ \dashrightarrow \sf 3 \bigg\lgroup \sf{ 12 \:+ \:4 }\bigg\rgroup =\bigg\lgroup \sf{ 44 \:+ \:4 }\bigg\rgroup \\\\ \dashrightarrow \sf 3 \bigg\lgroup \sf{ 12 \:+ \:4 }\bigg\rgroup =\bigg\lgroup \sf{ 48 }\bigg\rgroup \\\\ \dashrightarrow \sf 3 \bigg\lgroup \sf{ 16 \:\: }\bigg\rgroup =\bigg\lgroup \sf{ 48 }\bigg\rgroup \\\\\dashrightarrow \sf \bigg\lgroup \sf{ 48 \:\: }\bigg\rgroup =\bigg\lgroup \sf{ 48 }\bigg\rgroup \\\\ \dashrightarrow \sf{ 48 \:\: } =\sf{ 48 } \\\\ \dashrightarrow \underline {\boxed {\purple{\pmb{\frak{\:48 \:\: = 48 }}}}}$

⠀⠀⠀⠀⠀$\therefore {\underline {\pmb{\bf{ Hence, \:Verified \:}}}}$