Question

after 5 year the age of a father will be three times of the age of his son . 5 years ago he was 7 times as old as his son was . what was present ages

Answer 1

AnswEr :

Let the Present Age of Father be n yrs and Present Age of Son be m yrs.

• According to the Question Now :

⋆ After 5 year the age of a father will be three times of the age of his son.

⇝ Father = 3 times of Son

⇝ (n + 5) = 3 × (m + 5)

⇝ n + 5 = 3m + 15

⇝ n = 3m + 15 - 5

⇝ n = 3m + 10 —eq. ( I )

⋆ 5 years ago he was 7 times as old as his son was.

⇝ Father = 7 times of Son

⇝ (n - 5) = 7 × (m - 5)

⇝ (3m + 10 - 5) = 7 × (m - 5) —[ from I ]

⇝ 3m + 5 = 7m - 35

⇝ 35 + 5 = 7m - 3m

⇝ 40 = 4m

• Dividing Both term by 4

⇝ m = 10 Yrs. [ Son Present Age ]

• Putting the Value of m in ( I )

⇝ n = 3m + 10

⇝ n = 3 × 10 + 10

⇝ n = 30 + 10

⇝ n = 40 Yrs. [ Father Present Age ]

∴ Hence, Present Age of Father is 40 Years and Present Age of Son is 10 Years.

Answer 2

Answer:

$\large\bold\red{Father's \:Present \:Age=40\:yrs.}\\\\\large\bold\red{Son's \:Present\: Age = 10 yrs.}$

Step-by-step explanation:

Let,

The present age of Father is 'x' yrs.

And,

The present age of son is 'y' yrs.

Now,

After 5 Years

Age Of father = (x+5) yrs.

And,

Age of son = (y+5) yrs.

But,

According to question,

Father will be 3 times of the age of his son.

Therefore,

We have the following equation,

$= > x + 5 = 3(y + 5) \\ = > x + 5 = 3y + 15 \\ = > x - 3y - 10 = 0 \: \: \: \: ......(i)$

Now,

Before 5 Years,

Age of father = (x-5) yrs.

And,

Age of son = (y-5) yrs.

But,

According to Question,

Father would be 7 times the age of his son.

Therefore,

We have the following Equation,

$= > x - 5 = 7(y - 5) \\ = > x - 5 = 7y - 35 \\ = > x - 7y + 30 = 0 \: \: \: \: .......(ii)$

Now,

Subtracting eqn (i) from (ii),

We get,

$= > ( x - 7y + 30) - (x - 3y - 10) = 0 \\ = > - 7y + 3y + 30 + 10 = 0 \\ = > - 4y + 40 = 0 \\ = > 4y = 40 \\ = > y = 10$

Now,

Putting this value of y = 10, in eqn (ii),

We get,

$= > x - (7 \times 10) + 30 = 0 \\ = > x - 70 + 30 = 0 \\ = > x - 40 = 0 \\ = > x = 40$

Hence,

Present age of father = 40 yrs.

Present age of his son = 10 yrs.