Question

Example 3.1 The father's age is six times his son's age. Six years hence the age of father
will be four times his son's age. Find the present ages (in years) of the son and father.​

Answer 1

Answer:

Correct Question :

The father's age is six times his son's age . Six years hence the age of the father will be four times his son's age . Find the present age of the son and father ( in years ) .  

Solution :  

Let the present age of son be  x  

So , Father's present age = 6x  

Six years hence the age of the father will be four times his son's age .  

⇒ ( 6x + 6 ) = 4 ( x + 6 )  

⇒ 6x + 6 = 4x + 24  

⇒ 6x - 4x = 24 - 6

⇒ 2x = 18  

⇒ x = 9    

Present age of son ,  

x = 9 years  

Present age of father ,  

6x = 6(9)= 54 years  

Step-by-step explanation:

thanks..

Answer 2

Question:

• The father's age is six times his son's age. Six years hence, the age of the father will be four times his son's age. The present ages in years of the son and the father are respectively.

Answer:

• The present ages of father and his son is 54 and 9 years respectively.

Step-by-step Explanation:

Given:

• Age of father is six times age of his son. 
• Four years hence or after four years.
• The age of father will be four times his son's age.

To find:

• Their present ages?

Solution:

❍ So, Let's consider age of his son be x years and father be 6x years.

______________________________________

☆ After four years,

• Age of Son = (x + 6) years
• Age of father = (6x + 6) years⠀

Now,⠀

$\begin{gathered}\qquad {\color{indigo}{\bigstar}}\: {\underline{\pmb{\frak{{According~to~the~Question~:}}}}}\\\\\ \qquad :\implies\sf Father's\:age = 4 \bigg(Son's\:age \bigg)\\\\\\ \qquad:\implies\sf 6x + 6 = 4 \bigg(x + 6 \bigg)\\\\\\ \qquad:\implies\sf 6x + 6 = 4x + 24\\\\\\ \qquad:\implies\sf 6x - 4x = 24- 6\\\\\\ \qquad:\implies \sf 2x = 18\\\\\\ \qquad:\implies\sf x = \cancel{\dfrac{18}{2}}\\\\\\ \qquad:\implies{\underline{\boxed{{\frak{x = 9}}}}}\pink\bigstar\\\\\end{gathered}$

Therefore,⠀⠀

• Age of Son, x = 9 years
• Age of his father, 6x = 54 years

$\\ \therefore\:{\underline{\sf{Hence,\:Present\:Age\:of\:father\:\&\:his\:son\:is\:{\textsf{ \textbf{54 }}} \: \sf{and} \: \textsf{\textbf{9\:years}} \: \sf{respectively.}}}}$

Thank you :)

||TheUnkownStar||