Question

Mother is 5 times as old as her daughter. 4 years ago, mother was 9 times as old as her daughter. Find the present age?

Answer 1

$\huge{{\huge{\boxed{\huge{\red\star\mathfrak\purple{\large{\underline{\underline{ Answer! }}}}}}}}}$

$\textsf{Let the age of daughter be x}$

$\textsf{Then,mother's age= 5x}$

Now, 4 years ago,

$\textsf{Age of daughter 4 years ago= (x-4)}$

$\boxed{ \textsf{Age \: of \: mother \: 4 \:years ago= 9(x - 4)}}$

= 9x-36

Then,

Present age of mother= 9x-36+4

=9x-32

Now,

5x= 9x-32

⟹5x-9x= -32

⟹-4x= -32

⟹4x= 32

$\boxed{ \red{\bold{ \implies \: x = \frac{32}{4} }}}$

$\boxed{ \red{ \bold{⟹x = 8}}}$

$\textsf{Mother's age= 5x= 5(8)= 40 years}$

$\textsf{Daughter's age= x= 8 years}$

Answer 2

✬ Mother age = 40 years ✬

✬ Daughter age = 8 years ✬

Step-by-step explanation:

Given:

• Mother is 5 times as old as her daughter.
• 4 years ago mother was 9 times as old her daughter.

To Find:

• What is the present ages of mother and daughter ?

Solution: Let the present age of her daughter be x years. Therefore,

➨ Mother age = 5 times of x

➨ Mother age = 5x years

[ 4 years ago their ages ]

• Daughter's age = (x – 4) years
• Mother's age = (5x – 4) years

A/q

• 4 years ago mother was 9 times as old her daughter.

$\implies{\rm }$ (5x – 4) = 9(x – 4)

$\implies{\rm }$ 5x – 4 = 9x – 36

$\implies{\rm }$ 5x – 9x = – 36 + 4

$\implies{\rm }$ – 4x = – 32

$\implies{\rm }$ 4x = 32

$\implies{\rm }$ x = 32/4

$\implies{\rm }$ x = 8

So,

➯ Present age of daughter = x = 8 years

➯ Present age of mother = 5x

=> 5(8) = 40 years