Question

Father is four times the age of his daughter. If after 5 years, he would be threee times of daughter’s age, then further after 5 years, how many times he would be of his daughter’s age

Answer 1

$\huge\mathfrak\blue{Answer:}$

Given:

• We have been given that Father age is 4 times the age of his daughter
• After 5 Years Father would be 3 times of daughter’s age

To Find:

• We need to find that after 10 years, The Father would be how many times of her daughter

Solution:

Let the age of Daughter = x

Age of her Father = 4x

$\sf{\orange {After \: 5 \: years}}$

Age of Daughter = ( x + 5 ) years

Age of her Father = ( 4x + 5 ) years

_______________________________

According to the Question

$\longrightarrow \sf{ (Age \: of \: After) = 3 \times (Age \: of \: Daughter) }$

$\longrightarrow \sf{ (4x+5) = 3 \times (x+5) }$

$\longrightarrow \sf{ 4x + 5 = 3x + 15}$

$\longrightarrow \sf{ 4x - 3x = 15 - 5}$

$\longrightarrow \sf{ x = 10 }$

$\boxed{\sf{\orange{Present \: Age \: of \: Daughter = 10 \: Years }}}$

$\implies \sf{Age \: of \: Father = 4 \times x}$

$\implies \sf{ 4 \times 10 }$

$\implies \sf{40 \: years}$

$\boxed{\sf{\orange{Present \: Age \: of \: Father = 40 \: years }}}$

________________________________

After Further 5 years $\implies$ 10 years

$\implies$ Age of Daughter = 10 + 10 = 20

$\implies$Age of father = 40 + 10 = 50

Dividing the age of Father by Daughter

$\implies \sf{ \frac{Age \: of \: Father }{Age \: of \: Daughter } = \frac{50}{20}}$

$\implies \sf{ \frac{Age \: of \: Father }{Age \: of \: Daughter } = 2.5 }$

$\implies \sf{Age \: of \: Father = 2.5 \times Age \: of \: Daughter}$

$\boxed{\sf{\green{Age \: of \: Father \: will \: be \: 2.5 \: times \: of \: Daughter }}}$

________________________________

$\huge\mathfrak\red{Verification:}$

After 5 Years from present

$\implies \sf{Age \: of \: Daughter = 10 + 5 = 15}$

$\implies \sf{Age \: of \: Father = 40 + 5 = 45 }$

$\implies \sf{Age \: of \: Father = 3 \times 15}$

$\boxed{\sf{\blue{Age \: of \: Father = 3 ( Age \: of \: Daughter) }}}$

Hence Verified !!

Answer 2

Let the age of daughter be x

let the age of father be 4x

after five year the age of daughter be (x+5)

and age of father be (4x+5)

A.T.Q.

4x+5=3 (x+5)

4x+5=3x+15

×=10

age of daughter =10

Age of father =4x+5

= 4×10+5

=45

Hope it help you

Mark as Brainliest