Question

A man is twice as old as his son. 20 years ago, the age of the man was 12 times the age of the son.
Find their present ages​

Answer 1

$\bigstar{ \huge{ \underline{ \underline{ \sf{AnSwer:}}}}}$

Let the age of son is x year's.

It is given that the man is twice as old as his son. So,

Let the age of man is 2x year's.

Now,

★ According to the question,

20 years ago, the age of the man was 12 times the age of the son. So,

$: \implies \sf \: \: 2x - 20 = 12 \times (x - 20) \\ \\ : \implies \sf \: \:2x - 20 = 12x - 240 \\ \\ : \implies \sf \: \:240 - 20 = 12x - 2x \\ \\ : \implies \sf \: \:220 = 10x \\ \\ : \implies \sf \: \:x = \dfrac{220}{10} \\ \\ : \implies \sf \: \:{ \underline{ \boxed{ \sf{ \purple{x = 22 \: years \: }}}}} \: \bigstar$

So,

• The present age of son is 22 year's.

★ Present age of man =

$: \implies \sf \: \:2 \times x \\ \\: \implies \sf \: \:2 \times 22 \\ \\ : \implies \sf \: \:{ \underline{ \boxed{ \sf{ \red{44 \: years}}}}} \: \bigstar$

$\therefore$Present age of son is 22 year's while present age of man is 44 year's.

Answer 2

Answer:

Step-by-step explanation:

Given :-

A man is twice as old as his son.

20 years ago, the age of the man was 12 times the age of the son.

To Find :-

The Present Age

Solution :-

Let son's present age be x years

And the father's present age be 2x years

20 years ago

Son's age be x - 20 years

And father's age be 2x - 20 years

According to the Questions

⇒ 12 (x - 20) = 2x - 20

⇒ 12x - 240 = 2x - 20

⇒ 12x - 2x = 240 - 20

⇒ 10x = 220

⇒ x = 220/10

⇒ x = 22

Present age of son = x = 22 years

Present age of father = 2x = 2 × 22 = 44 years