Answer:

Given that:

1) Father's age is 5 times his son .

2) And Father's age will be thrice his son's age after 6 years.

To find.

The present age of his son.

Solution:

Let Present Age of father be ' x ' & Age of his son be ' y '.

Then,

⇒ x = 5\times yx=5×y - (i)

After six years their age will be " x + 6 " & " y + 6" respectively.

⇒ (x+6) = 3(y+6)(x+6)=3(y+6)

⇒ x + 6 = 3y + 18x+6=3y+18

⇒ x = 3y +18-6 = 3y+12x=3y+18−6=3y+12 - (ii)

Now by equating x from equation (i) & (ii) we get.

⇒ 5y = 3y+125y=3y+12

⇒ 5y - 3y =125y−3y=12

⇒ 2y = 122y=12

⇒

Therefore present age of the son is 6 years.

We know that,

Age of father = 5 y

= 5 × 6

= 30 years.

Therefore present age of father is 30 years.

Explanation:

son's age=x

father's age=y

according to 1st condition

5x=y_(1)

after six years

son's age =x+6

father's age=y+6

according to 2nd condition

y+6=3(x+6)

y+6=3x+18

-3x+y=18-6

-3x+y=12_(2)

substituting value of y from (1) in (2)

-3x+5x=12

2x=12/2

x=6

putting value of x in (1)

5×6=y

30=y

therefore, father's age is 30 yrs