Question

At present a father is 40 years older than his son. Twenty years ago, he was
five times older than his son. What is the present age of the son?

Answer 1

Given :-

• Present age of father is 40 years more than that of his son.
• 20 years before, he was 5 times older than his son.

To Find :-

• The present age of son.

Solution :-

Let:-

• The present age of son : x

Then,

• The present age of father : x + 40

Now, 20 years ago, the son's age would be x - 20 and his father's age would be x + 20.

Account to the question,

$\implies\rm{x+20=5(x-20)}$

$\implies\rm{x+20=5x-100}$

$\implies\rm{20+100=5x-x}$

$\implies\rm{4x=120}$

$\implies\rm{x=\dfrac{120}{4}}$

$\implies\rm{x=}\:\bold{30}$

Hence,

• The present age of son (x) = 30 years.

Also,

• The present age of father = x + 40 = 70 years.

Answer 2

✯✯ QUESTION ✯✯

At present a father is 40 years older than his son. Twenty years ago, he was five times older than his son. What is the present age of the son?

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✰✰ ANSWER ✰✰

$\longrightarrow{Let\:Present\:Age\:of\:Son=x}$

$\longrightarrow{Let\:Present\:Age\:of\:Father=x+40}$

As given that Twenty Years ago father was five times older than his son...So,

$\longrightarrow{Son's\:Age=x-20}$

$\longrightarrow{Father\:Age=x+20}$

A.T.Q : -

$\longrightarrow{x+20=5(x-20)}$

$\longrightarrow{x+20=5x-100}$

$\longrightarrow{x-5x=-100-20}$

$\longrightarrow{-4x=-120}$

$\longrightarrow{x=\cancel\dfrac{-120}{-4}}$

$\longrightarrow{\large{\boxed{\bold{\bold{\green{\sf{x=30}}}}}}}$

So ,

$\longrightarrow{Present\:Age\:of\:Son=x}$

$\longrightarrow{\textbf{30\:years}}$

$\longrightarrow{Present\:Age\:of\:Father=x+40}$

$\longrightarrow{30+40}$

$\longrightarrow{\textbf{70\:years}}$