Question

Arvind is six times as old as his son. after twenty years he will be only twice old as his son. find their present ages.​

Answer 1

Step-by-step explanation:

Assuming Arvind's sons age x years.

Then Arvind's age = 6x years

After 20 years :

➡ Sons age = x+20 years

➡ Arvind's age = 6x + 20 years.

According to the question :

=> 6x + 20 = 2(x + 20)

=> 6x + 20 = 2x + 40

=> 4x = 20

=> x = 5 (sons age)

Then Arvind's age = 25 years

Answer 2

GiveN:-

Arvind is six times as old as his son. after twenty years he will be only twice old as his son.

To FinD:-

Their present ages.

SolutioN:-

• Let the present age of the son be x.
• Let the present age of Arvind be 6x.

After 20 years,

1. Age of the son will be (x + 20) years.
2. Age of Arvind will be (6x + 20) years.

It is said that after twenty years Arvind will be twice old as his son.

According to the question,

$\large\implies{\sf{6x+20=2(x+20)}}$

$\large\implies{\sf{6x+20=2x+40}}$

$\large\implies{\sf{6x-2x=40-20}}$

$\large\implies{\sf{4x=20}}$

$\large\implies{\sf{x=\dfrac{20}{4}}}$

$\large\implies{\sf{x=\dfrac{\cancel{20}}{\cancel{4}}}}$

$\large\therefore\boxed{\bf{x=5.}}$

The ages:-

• Age of son = x = 5 years.
• Age of Arvind = 6x = 6 × 5 = 30 years.

Therefore,

The present ages of Arvind and his son is 30 years and 5 years respectively.