Question

Mother is 20 years older than her son ten years ago she was three times as old as a son then ,find the present ages.

Answer 1

Answer :

The age of mother is 40 years and that of her son is 20 years

$\large{\underline{\bf{Given:}}}$

• Mother is 20 years older than her son
• 10years ago she was three times as old as her son

$\large{ \underline{ \bf{To \: Find : }}}$

• Their present ages

$\large{ \underline{ \bf{Solution : }}}$

Let us consider the son's age be x and his mother's age be x+20

$\sf \underline{ \underline{ \dag \: \: According \: to \: question : }}$

$\sf\implies x +20 - 10 = 3(x - 10) \\\\ \sf\implies x + 10 = 3x - 30 \\\\ \sf\implies x - 3x = -30 - 10 \\\\ \sf\implies -2x = -40 \\\\ \sf\implies x = 20$

Since , mother's age was x + 20

➜ 20 + 20

➜ 40 years

Therefore , the age of son is

20 years and that mother is 40 years

Answer 2

Given that ,

• The present age of mother is 20 years older than her son

• Ten years ago , the age of mother was 3 times as old as a son

Let , the present age of son be " x "

According to the question ,

Age of mother = x + 20 ---- (i)

And

(Age of mother - 10) = 3 × (x - 10)

Thus ,

(x + 20) - 10 = 3x - 10 { from eq (i) }

x + 10 = 3x - 30

2x = 40

x = 20

Put the value of x = 10 in eq (i) , we get

Age of mother = 20 + 20

Age of mother = 40

$\sf \therefore \underline{The \: present \: ages \: of \: mother \: and \: her \: son \: are \: 40 \:years \: and \: 20 \: years}$