Question

At present the sum of monica age and her daughter age is 44 years. After 2 years monica age will be three times that of her daughter's age . Find their present ages.​

Answer 1

Monica = 34 Years

Daughter = 10 Years

Step-by-step explanation:

Given:

• Sum of Monica and her daughter age is 44 years.
• After 2 years Monica's age will be 3 times that of daughter's age.

To Find:

• What are their present ages ?

Solution: Let present ages of Monica & her daughter be x and y years respectively. Therefore,

Monica + daughter = 44

x + y = 44

x = (44 – y).........1

Now after 2 years their ages will be

• Monica's age = (x + 2) years
• Daughter's age = (y + 2) years

A/q

• After 2 years Monica's age will be 3 times that of daughter's age.

$\implies{\rm }$ (x + 2) = 3(y + 2)

$\implies{\rm }$ (44 – y + 2) = 3y + 6

$\implies{\rm }$ 46 – y = 3y + 6

$\implies{\rm }$ 46 – 6 = 3y + y

$\implies{\rm }$ 40 = 4y

$\implies{\rm }$ 40/4 = y

$\implies{\rm }$ 10 = y

So their present ages are

• Daughter's present age is y = 10 years.

• Monica's present age is x = 44 – 10 = 34 years.

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

VERIFICATION

x + y = 44 [eq(i)]

where,

• x = 34 yrs
• y = 10 yrs

put these values in eq(i)

➛ 34 + 10 = 44

➛ 44 = 44

Hence, our answer is Verified.