Question

At present, the sum of Monica's age and her daughter's age is 44 yrs. After 2 years Monica's age will be 3 times that of her daughter's age. Find their present ages.

Answer 1

let the age of Monica be x
let the age of monica's daughter be 44-x
x+2=(44-×+2)3
x+2=(46-x)3
x+2=138-3x
x+3x=138-2
4x=136
×=34
Monica age=34
her daughter age=10

Answer 2

❅GIVEN:

• The sum of present ages of Monica and her daughter = 44 years
• After 2 years Monica age will be 3 times that of her daughter's age.

❅TO FIND:

• What were their present ages = ?

❅SOLUTION:

Let, the present age of Monica be x yrs

and her daughter's age be y yrs

Now,

$\mathbb{ACCORDING \: TO \: QUESTION}$

x + y = 44 ...........(i)

2 + x = 3(2 + y)

= 2 + x = 6 +3y ............(ii)

Now, in eq.(i)

$\sf \to x + y = 44$

$\sf \to x = 44 - y$

Put the value of x in eq(ii) we got

$\sf \to 2 + x = 6 + 3y$

$\sf \to 2 + (44 - y) = 6 + 3y$

$\sf \to 2 + 44 -y= 6 + 3y$

collect like terms

$\sf \to 2 + 44 -6= 3y + y$

solve it

$\sf \to 40= 4y$

$\sf \to y = \frac{ \cancel{40}}{ \cancel{4}} = 10$

substitute the value of y in eq(i) we get

$\sf \to x + y = 44$

$\sf \to x + 10 = 44$

$\sf \to x = 34$

Hence, Present age of Monica will be 34 years

and

Present age of Monica's daughter will be 10 years