Question

10 years hence the age of the father is two times the age of his son. ten years ago the age 6 times of his son. find the present age​

Answer 1

Step-by-step explanation:

Answer for this question is above

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Answer 2

The present Age of Father is 40 years

The present Age of Son is 15 years

Step-by-step explanation:

Given as :

Statement I

10 years hence the age of the father is two times the age of his son .

Let The present Age of Father = F years

Let The present Age of Son = S years

So, After 10 years

The Age of Father = ( F + 10 ) years

The Age of Son = ( S + 10 ) years

From statement

After 10 years  the age of the father is two times the age of his son .

i.e      ( F + 10 ) = 2 ×   ( S + 10 )

or,       F + 10 = 2 S + 20

Or,       F - 2 S = 20 - 10

∴          F - 2 S = 10                           .............1

Again

Statement II

10 years ago the age of the father is six times the age of his son .

Let The present Age of Father = F years

Let The present Age of Son = S years

So, Before 10 years

The Age of Father = ( F - 10 ) years

The Age of Son = ( S - 10 ) years

From statement

After 10 ago  the age of the father is six times the age of his son .

i.e      ( F - 10 ) = 6 ×  ( S - 10 )

or,       F - 10 = 6 S - 60

Or,      6 S - F = 60 - 10

∴         6 S - F = 50                           .............2

Solvinf eq 1 and eq 2 , we get

( 6 S - F ) + ( F - 2 S ) = 5 0 + 10

Or,  ( 6 S - 2 S ) + ( - F + F ) = 60

Or,   4 S + 0 = 60

∴              S = $\dfrac{60}{4}$  = 15

i.e Age of Son = 15 years

Put The value of S into eq 2

∵   6 S - F = 50

or,    6 × 15 - F = 50

Or, F = 90 - 50

∴     F = 40 years

So, The Age of father = 40 years

Hence, The present Age of Father is 40 years

The present Age of Son is 15 years  Answer