Question

The sum of the present ages of a son and his father is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, what will be son's age? ​

Answer 1

❍ Given :-

• Sum of there present age is 60 years
• Six years ago, father's age was five times the age of the son

❍ To Find :-

• Son's age after 6 years

❍ Solution :-

Let the present age of son be x.

Then, present age of father is (60 - x).

According to the question,

$\tt →(60 - x) - 6 = 5(x - 6)$

$\tt →54 - x = 5x - 30$

$\tt →54 + 30 = 5x + x$

$\tt →84 = 6x$

$\tt →x = \dfrac{\cancel{84}}{\cancel{6}}$

$\tt →\fbox{x = 14}$

∴ Son's age after 6 years = (x + 6) years

= (14 + 6) years

= 20 years

Therefore, after 6 years sons age is 20 years.

Answer 2

Corrected Question :

• The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, what will be son's age ?

$~$

${ \underline{ \underline {\red{ \star} { \textsf {\textbf{ Given :}}}}}}$

• Sum of there present age is 60 years.
• Six years ago, father's age was five times the age of the son.

$~$

${ \underline{ \underline {\red{ \star} { \textsf {\textbf{ To~Find :}}}}}}$

• After 6 years
• Find the son's age ?

$~$

${ \underline{ \underline {\red{ \star} { \textsf {\textbf{ Solution :}}}}}}$

• Let the son's present age be x years.
• Father's present age will be (60 - x) years.

$~$

$\dag ~\underline{\frak{\pmb{According~ to ~the ~given ~question~:}}}$

$~$

$\qquad{\sf:\implies{(60~-~x)~-~6~=~5(x~-~6)}}$

$~$

$\qquad{\sf:\implies{54~-~x~=~5x~-~30}}$

$~$

$\qquad{\sf:\implies{6x~=~84}}$

$~$

$\qquad{\sf:\implies{x~=~\cancel\dfrac{84}{6}}}$

$~$

$\qquad:\implies{\underline{\boxed{\frak{\pink{\pmb{x~=~14}}}}}}$★

$~$

Hence,

• The age of his son after 6 years will be (x + 6) years = 20 years.