Question

21. 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

Given: A man is twice as old as his son. Let the present age of the son be x years.

Therefore,

• Man's age = (2x) years.

A/Q,

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

⠀

Therefore,

⠀⠀

$\longrightarrow\sf 2x - 20 = 12(x - 20) \\\\\\\longrightarrow\sf 2x - 20 = 12x - 240 \\\\\\\longrightarrow\sf 10x = 220\\\\\\\longrightarrow\sf x = \cancel\dfrac{220}{10}\\\\\\\longrightarrow{\underline{\boxed{\frak{x = 22}}}}\;\bigstar$

⠀

Hence,

⠀

• Age of son, x = 22 years.

• Man's age, 2x = 2(22) = 44 years.

⠀

$\therefore{\underline{\sf{Hence, \; their\; present\; ages \; are\; \bf{22\;years\;\&\;44\;years. }.}}}$

Answer 2

Answer:

Given :-

• A man is twice as old as his son. 20 years ago, the age of man was 12 times the age of the son.

To Find :-

• What are their present ages.

Solution :-

Let, the present age of son be x years

And, the present age of man will be 2x years

According to the question,

⇒ $\sf 12(x - 20) =\: 2x - 20$

⇒ $\sf 12x - 240 =\: 2x - 20$

⇒ $\sf 12x - 2x =\: - 20 + 240$

⇒ $\sf 10x =\: 220$

⇒ $\sf x =\: \dfrac{\cancel{220}}{\cancel{10}}$

➠ $\sf\bold{\purple{x =\: 22\: years}}$

Hence, the required ages are,

✧ Present age of son = x = 22 years

✧ Present age of man = 2x = 2 × 22 = 44 years

$\therefore$ The present age of son is 22 years and the present age of man is 44 years.

${\red{\boxed{\large{\bold{VERIFICATION :-}}}}}$

↦ $\sf 12(x - 20) =\: 2x - 20$

↦ $\sf 12x - 240 =\: 2x - 20$

By putting x = 22 we get,

↦ $\sf 12(22) - 240 =\: 2(22) - 20$

↦ $\sf 12 \times 22 - 240 =\: 2 \times 22 - 20$

↦ $\sf 264 - 240 =\: 44 - 20$

↦ $\sf 24 =\: 24$

➦ LHS = RHS

Hence, Verified ✔