Question

a mother is four times as old as her daughter. in two years, the sum of their ages will be 44. how old is the mother now?

a- 30
b- 32
c- 34
d- 36
e- 38

Answer 1

Given :-

A mother is four times as old as her daughter. in two years, the sum of their ages will be 44

To Find :-

Age of mother

Solution :-

Let their present age of daughter be x and age of mother be y

After 2 years

$\sf:\implies Age\;of\;daughter = x+2$

$\sf:\implies Age\;of\; mother = y + 2$

Now, It is also given that mother is 4 times as his son

$\sf:\implies 4x=y(i)$

Their sum after 2 years is 44

$\sf:\implies x+2+y+2 = 44$

$\sf:\implies x+y+4=44$

$\sf:\implies x+y=44-4$

$\sf:\implies x+y=40$

Subsituting value of y from Eq. 1

$\sf:\implies x+4x=40$

$\sf:\implies 5x=40$

$\sf:\implies x=\dfrac{40}{5}$

$\sf:\implies x=8$

Using Eq. 1 again to find age of mother

$\sf:\implies 4x=y$

$\sf:\implies 4(8)=y$

$\sf:\implies 32=y$

${\textsf{\textbf{\underline{Therefore, Age of mother is 32 years.}}}}$

Option B is correct

Answer 2

Answer => Option - (b) :-

Let :-

• The present age of mother = 4x
• The present age of daughter = x

Given :-

• Sum of mother and her daughter age = 44

To Find :-

• The present age of mother = ?

Solution :-

• To calculate the age of mother at first we have to set up equation by taking clue in the question. As given in the question are a mother is four times as old as her daughter. in two years, the sum of their ages will be 44.

Calculation begins :-

• After two years their age is 44

⟹ Mother's age + Daughter's age = 44

⟹ (4x + 2) + (x + 2) = 44

⟹ 5x + 4 = 44

⟹ 5x = 44 - 4

⟹ 5x = 40

⟹ x = 8

• Now calculate their age here :-

⟹ The mother's age (4x) = 4(8) = 32 years

⟹ The daughter's age (x) = 8 years

Therefore , The present age of mother (4x) = 32 years