Question

The father's age is six times his son's age. Four years hence, the age of the father is four times his son's age. Find the present age of the son and his father respectively.​

Answer 1

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★Present age of father is 36 yr and age of son is 6 yr.

Given

• The father's age is six times his son's age. Four years hence, the age of the father is four times his son's age

To find

•  the present age of the son and his father respectively

Calculation

Let x yr be the present age of father and y yr be the present age of son.

Four years hence, it has relation by given condition,

(x + 4) = 4(y + 4)

• ⇒ x-4y = 12 ------------(i)

and ,The present condition of their ages is

• x = 6y ------------(ii)

On putting the value of x from Eq. (ii) in Eq. (i), we get

• 6y-4y=12
• ⇒ 2y = 12
• ⇒ y = 6

When y = 6, then x = 36

Hence, present age of father is 36 yr and age of son is 6 yr.

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Answer 2

❁GIVEN QUESTION❁

The father's age is six times his son's age. Four years hence, the age of the father is four times his son's age. Find the present age of the son and his father respectively.

LET'S UNDERSTAND WHAT WE HAVE TO DO !

It is given to us that the age of father's is six times his son's age. so in order to find there ages we will assume their ages as a ( father age ) and b ( son's age )

Now it is given that after 4 years the age of father (a) is four times then his son's age (b). 

and finally we have to Find the present age of the son and his father respectively.

NOW ACCORDING TO THE QUESTION LET'S SOLVE !

Father's age is six times his son's age

→ a = 6b ....(1)

After four year the age of the father is four times his son's age

→ a + 4 = 4 × ( b + 4 ) ....(2)

now we can see that we have got two equations.. so let's simplify (2nd equation) !

→ a + 4 = 4 × ( b + 4 )

→ a + 4 = ( (4 × b) + (4 × 4 ) )

→ a + 4 = ( 4b ) + ( 16 )

→ a - 4b = 16 - 4

→ a - 4b = 12

now the first equation that we have got is → a = 6b, hence we will put the value of a = 6b

bye putting the value we got

→ 6b - 4b = 12 [ a = 6b (by 1st equation)]

→ 2b = 12

→ b = 12/2

→ b = 6

Now we can see that the age of son (b) is 6 years , therefore according to the Question father's age is six times his son's age , the age of father will be 6b = 6 × 6 which is 36 years.

❀REQUIRED ANSWER❀

Age of son - 6 years

Age of father - 36 years