Question

The age of a father is equal to sum of the ages of his 6 children.After 15 years,twice the age of the father will be equal to the sum of ages of his children.Find the age of the father.​

Answer 1

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$\huge\sf\red{Given\::-}$

• $\large\sf\orange{The \ age \ of \ a \ father \ is \ equal \ to \ sum \ of \ the \ ages \ of \ his \ 6 \ children.}$

• $\large\sf\blue{After \ 15 \ years, \ twice \ the \ age \ of \ the \ father \ will \ be \ equal \ to \ the \ sum \ of \ ages \ of \ his \ children.}$

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$\huge\sf\red{To\:Find\::-}$

• $\large\sf\orange{Find \ the \ age \ of \ the \ father.}$

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$\huge\sf\red{Solution\::-}$

$\sf\orange{Let,}$

• $\large\sf\green{Father's\:age\:=\:x}$

• $\large\sf\green{Ages\:of\: six \:children\:=\:x_1 ,\: x_2 ,\: x_3 ,\: x_4 ,\: x_5 ,\: x_6 }$

$\to\:\sf\purple{x \:=\:x_1 \: +\:x_2 \: +\:x_3 \: +\:x_4 \: +\:x_5 \: +\:x_6 ......(1)}$

$\sf\orange{After\:15\: years}$

$\to\:\sf\blue{2(x+15) \:=\:x_1 + 15\:+\:x_2 + 15\:+\:x_3 + 15\:+\:x_4 + 15\:+\:x_5 + 15\:+\:x_6 + 15}$

$\to\:\sf\purple{2x+30\:=\:x+6(15)}$

$\to\:\sf\blue{2x-x\:=\:90-30}$

$\to\:\sf\underline\pink{x \:=\:60}$

$\sf\orange{Hence,}$

$\star\:\sf\underline\red{Present\:age\:of\: father\:is\:60\:years}$

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