Question

A man is 4 times as old as his son. After 16 years, he will be twice the age of his sum .Find the present age of son and man.​

Answer 1

$\star \; {\underline{\boxed{\pmb{\pink{\sf{ \; Given \; :- }}}}}}$

• A man is 4 times as old as his son
• After 16 years ,he will be twice the of his son .

$\star \; {\underline{\boxed{\pmb{\blue{\sf{ \; To \; Find \; :- }}}}}}$

• Preasent age = ?

$\star \; {\underline{\boxed{\pmb{\red{\sf{ \; SolutioN \; :- }}}}}}$

⚘ According to the Question :

$\longmapsto$ Let the age of son be y .So,

$\qquad \; {\pmb{\frak{ Present \; Age \; of \; Son = y }}}$

$\longmapsto$ Son is 4 times the age of Son .So,

$\qquad \; {\pmb{\frak{ Present \; Age \; of \; Man = 4y }}}$

$\longmapsto$ Age of son 16 years later is two times the age of son .So,

$\qquad \; {\frak{ \bigg( 4y + 16 \bigg) = 2 \bigg( y + 16 \bigg) }}$

$\\ \qquad{\rule{150pt}{1pt}}$

⚘ Calculating the Value of y :

${\dashrightarrow{\qquad{\sf{ \bigg( 4y + 16 \bigg) = 2 \bigg( y + 16 \bigg) }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ \bigg( 4y + 16 \bigg) = \bigg( 2y + 32 \bigg) }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 4y - 2y = 32 - 16 }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 2y = 16 }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ y = \dfrac{16}{2} }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ y = \cancel\dfrac{16}{2} }}}} \\ \\ \\ \ {\qquad \; \; {\therefore \; {\underline{\boxed{\purple{\pmb{\frak{ y = 8 }}}}}}}}$

$\\ \qquad{\rule{150pt}{1pt}}$

⚘ Calculating the Ages :

• Son = y = 8 years
• Man = 4y = 4(8) = 32 years

$\\ \qquad{\rule{150pt}{1pt}}$

⚘ Therefore :

❛❛ Age of son is 8 years and age of the man is 32 years . ❜❜

$\\ {\underline{\rule{300pt}{9pt}}}$

Answer 2

Step-by-step explanation:

Let the present age of the son be x years. As the man is 4 times as old as his son, the present age of the man will be (4x) years. or, 4x − 2x = 32 − 16 [Transposing 16 to the R.H.S. and 2x to the L.H.S.]

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