Question

At present the age of the father is 3
times the age of his son, 9 years
hence the father's age would be
twice that of his son. What is the
sum of the present ages of father
and his son?​

Answer 1

Answer :-

$\bf\huge\boxed{36}$

Explanation :-

Given :

• Age of father = Three times the age of his son
• After 9 years, Age of father = Twice the age of son

To find :

The sum of the present ages of father and his son.

Solution :

Let the present age of son be x

an the present age of father be 3x

After 9 years,

Age of son = (x + 9) years

Age of father = (3x + 9) years

According to question,

$= > 3x + 9 = 2( x+ 9)$

$= > 3x + 9 = 2x + 18$

$= > 3x - 2x = 18 - 9$

$= > x = 9$

Hence, the value of x is 9.

Now,

The present age of son (x) = 9 years

The present age of father (3x) => 3 × 9 = 27 years

Therefore, Sum of their ages :-

= (Age of father + Age of son)

= (27 + 9)

= 36

Hence, the sum of the ages of father and son is 36 respectively.

Answer 2

• Let present age of son be M.

» At present the age of the father is 3

times the age of his son.

• Age of father = 3M

» 9 years hence the father's age would be twice that of his son.

A.T.Q.

=> 3M + 9 = 2(M + 9)

=> 3M + 9 = 2M + 18

=> 3M - 2M = 18 - 9

=> M = 9

So ..

• Present age of son = 9 years (M)

• Present age of father = 27 years (3M)

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Sum of ages = Present age of son + Present age of father

=> 9 + 27 = 36 years

_________ [ ANSWER ]

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✡ Verification :

3M + 9 = 2(M + 9)

Put value of M = 9 in above equation

→ 3M + 9 = 2M + 18

→ M = 9

→ 9 = 9

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