Question

Aman's age is three times his son's age. Ten years ago he was five times his son's age. Find their present ages.​

Answer 1

Solution

Given :-

• Aman's age is three times his son's age.
• Ten years ago he was five times his son's age

Find :-

• Age of Aman & his son

Explanation

Let,

• Age of Aman = x years
• Age of his son = y years

Case(1).

(Aman's age is three times his son's age.)

➡ x = 3y

➡ x - 3y = 0_________(1)

Case(2).

(Ten years ago he was five times his son's age)

➡ (x-10) = 5 × (y-10)

➡x - 5y = -50 + 10

➡x - 5y = -40_________(2)

Sub. equ(1) & equ(2)

➡ -3y + 5y = 0 + 40

➡2y = 40

➡y = 40/2

➡y = 20

Keep value of y in equ(1)

➡x - 3 × 20 = 0

➡x = 60

Hence

• Present age of Aman = 60 years
• Present age of his son = 20 years

__________________

Answer 2

$\underline{\underline{\orange{\textbf{Step - By - Step - Explanation : -}}}}$

To Find :

• We need to find their present ages.

Sᴏʟᴜᴛɪᴏɴ :

$\sf{Let}\begin{cases}\sf{\bullet\: Aman's \:Age\: be\: x\: years}\\\sf{\bullet\:Aman's\: son's\: age\: be\: y\: years}\end{cases}$

$\underline{ \large \purple{ \mathscr{\dag\:A \bf{ccourding} \: to \: \mathscr {Q} \bf{uestion} ....}}}$

As it is given in the Question that Aman's age is three times his son's age.

So,

• Aman's Age = 3 × his son's age
• Aman's Age (x) = 3y ....(1)

Ten Years Ago :

Ten years ago Aman was five times his son's age.

• Aman's Son's age = y - 10
• Aman's Age = 5(y- 10) .....(2)

›› 3y - 10 = 5(y - 10)

›› 3y - 10 = 5y - 50

›› 50 - 10 = 5y - 3y

›› 40 = 2y

›› y = 40/2

›› y = 20

• Substituting value of y in (1)

›› x = 3y

›› x = 3 × 20

›› x = 60

$\large\dag \large { \red{\underline{\bf{Hence }}}}$

• Aman's Age x = 60 years
• His Son's age y = 20 years