Question

4 years ago Seema’s age was 3 times the age of her son. The sum of their ages 4 years ago was 48 years. Find their present age. ​

Answer 1

$\sf\large\underline\purple{Let:-}$

$\sf{\implies The\: present\:age\:_{(Seema)}=x}$

$\sf{\implies The\: present\:age\:_{(his\:son)}=y}$

$\sf\large\underline\purple{To\:Find:-}$

$\sf{\implies The\: present\:age\:_{(their)}=?}$

$\sf\large\underline\purple{Solution:-}$

To calculate the present age of Seema and his son, at first we have to set up equation as per the given clue in the question then solve those equation by solving we get the value of x and y where x is the age of Seema and y of his son.

$\sf\small\underline\red{Given\:in\:case\:(i):-}$

$\sf{\implies Seema's\:age\:_{(4\: years\:ago)}=3*Son's\:age\:_{(4\: years\:ago)}}$

$\tt{\implies x-4=3(y-4)}$

$\tt{\implies x-4=3y-12}$

$\tt{\implies x-3y=-12+4}$

$\tt{\implies x-3y=-8------(i)}$

$\sf\small\underline\red{Given\:in\:case\:(ii):-}$

$\sf{\implies The\:sum\:of\: their\:age\:_{(4\: years\:ago)}=48}$

$\tt{\implies (x-4)+(y-4)=48}$

$\tt{\implies x+y-8=48}$

$\tt{\implies x+y=48+8}$

$\tt{\implies x+y=56------(ii)}$

• Now substracting eq (i) and (ii) here:-]

$\tt{\implies x-3y=-8}$

$\tt{\implies x+y=56}$

• By solving we get here:-]

$\tt{\implies -4y=-64}$

$\tt{\implies y=16}$

• Putting the value of y=16 in eq (i) :-]

$\tt{\implies x-3y=-8}$

$\tt{\implies x-3(16)=-8}$

$\tt{\implies x-48=-8}$

$\tt{\implies x=-8+48}$

$\tt{\implies x=40}$

$\sf\large{Hence,}$

$\sf{\implies The\: present\:age\:_{(Seema)}=40\: years}$

$\sf{\implies The\: present\:age\:_{(his\:son)}=16\: years}$

Answer 2

Step-by-step explanation:

Given : -

• 4 years ago Seema’s age was 3 times the age of her son.

• The sum of their ages 4 years ago was 48 years.

To Find : -

• Find their present age.

Solution : -

Let the present age of Seema's x the present age of son y

Then ,

According to the Question :

x - 3y = - 8 ........ ( 1 )

x + y = 56 .......... ( 2 )

substracting equ 1 and equ 2

x - 3y = - 8

x + y = 56

_________

- 4y = - 64

4y = 64

y = 64/4

y = 16

Putting all values in equ 1

x - 3y = - 8

x - 3 × 16 = - 8

x - 48 = - 8

x = - 8 + 48

x = 40

Verification : -

40 - 3 × 16 = - 8

40 - 48 = - 8

- 8 = - 8

Hence Verified

the present age of Seema's = 40 Year and present Age of son = 16 Year