Question

A man is 37 years old and his two sons are 8 years and 3 years old. After how many
years will he be twice as old as the sum of the ages of his sons?
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(In Explanation)​

Answer 1

❍ Let the number of years in which his age will be twice as old as the sum of his sons be x years respectively.

• Present age of Man is 37 years old and Present age of his first son is 8 years old and second one is 3 years old.

Therefore,

— In x years their ages;

• Age of Man = (37 + x)
• Age of First son = (8 + x)
• Age of younger son = (3 + x)

$\rule{250px}{.3ex}$

⠀⠀$\qquad\quad{\underline{ \underline{ \pink{\bigstar\:\frak{According \: to \: the \: Given \: Question :}}}}}$

⠀⠀

• The age of father will be twice as old as the sum of ages of his sons.

⠀⠀

Therefore,

⠀

★ Father's age = 2(Sum of ages of son) ★

⠀⠀

$:\implies\sf (37 + x) = 2\Big[(8 + x) + (3 + x)\Big]\\\\\\:\implies\sf 37 + x = 2 (11 + 2x) \\\\\\:\implies\sf 37 + x = 22 + 4x\\\\\\:\implies\sf 3x = 15\\\\\\:\implies\sf x = \cancel\dfrac{15}{3}\\\\\\:\implies{\underline{\boxed{\frak{\pink{x = 5}}}}}\;\bigstar$

⠀⠀

$\therefore{\underline{\textsf{After\;\textbf{5 years}\;his\;age\;will\;be\;twice\;as\;old\;sum\;of\;ages\;his\;sons.}}}$

Answer 2

Answer:

Given :-

• A man is 37 years old and his two sons are 8 years and 3 years old.

To Find :-

• After how many years will he be twice as old as the sum of the ages of his sons.

Solution :-

Let, the years will be twice as old as the sum of the ages of his sons will be x years

$\mapsto$ Age of man = 37 + x

$\mapsto$ Age of first son = 8 + x

$\mapsto$ Age of second son = 3 + x years

According to the question,

↦ $\sf 37 + x =\: 2\bigg((8 + x) + (3 + x)\bigg)$

↦ $\sf 37 + x =\: 2(11 + 2x)$

↦ $\sf 37 + x =\: 22 + 4x$

↦ $\sf x - 4x =\: 22 - 37$

↦ $\sf {\cancel{-}} 3x =\: {\cancel{-}} 15$

↦ $\sf 3x =\: 15$

↦ $\sf x =\: \dfrac{\cancel{15}}{\cancel{3}}$

➠ $\sf\bold{\red{x =\: 5\: years}}$

$\therefore$ After 5 years will be twice as old as the sum of the ages of his sons.