Question

A man is 37 years old as his two sons are 8 years and 3 years old respectively after how many years will he be twice as old as the sum of the ages of his sons.​

Answer 1

Answer:

5

Step-by-step explanation:

5years

2*21=42

so the answer is 5years

Answer 2

• ❍ 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) ★

⠀⠀

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

⠀⠀

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