Question

Q1.Five years hence, father’s age will be three times the age of his daughter. Five years ago,
father was seven times as old as his daughter. Their present ages are:​

Answer 1

Explanation:

Since,we don't Know their present ages so,Let assume their present ages some Variable.

Let present age of daughter be 'x'

present age of father be 'y'

Five years hence, age of daughter= x+5

Age of father = y+5

According to the question

=> y+5= 3(x+5)

=>y+5= 3x+15

=>y= 3x+10--------(1)

Five yeara ago,

Age of daughter= x-5

Age of father = y-5

According to the question

=>y-5= 7(x-5)

=>y-5=7x-35

=>y= 7x-30--------(2)

Substracting Equation 1 from 2

=>7x-30-(3x+10)= y-y

=>7x-30-3x-10=0

=>4x-40=0

=>4x= 40

=>x= 10

Put X's value into equation 1

=>y= 3x+10

=>y= 3(10)+10

=>y= 30+10=40

y=40

Therefore, Present age of daughter is 10 years

Present age of father is 40 years

Answer 2

Age of Father = 40 Years

Age of Daughter = 10 Years

Given Terms:

• Five years hence age of father will be 3 times the age of daughter.
• Five years ago father's age was seven times of daughter's age.

Need To Find:

• Present ages of both ?

Solution: Let the present age of father be x years and daughter be y years.

Five years ago their ages were

• Father's age = ( x – 5 ) years
• Daughter's age = ( y – 5 ) years

Five years hence their ages would be

• Father's age = ( x + 5 ) years
• Daughter's age = ( y + 5) years

According to the question → First case

➥ (x – 5) = 7 × (y – 5)

➥ x – 5 = 7y – 35

➥ x = 7y – 35 + 5

➥ x = 7y – 30... equation 1

According to the question → Second case

➥ (x + 5) = 3 × (y + 5)

➥ x + 5 = 3y + 15

➥ 7y – 30 + 5 – 15 = 3y

➥ – 40 = 3y – 7y

➥ – 40/–4 = y

➥ 10 = y

Now put the value of y in first equation.

=> x = 7 × 10 – 30

=> x = 40 Years

Required age of father and daughter is 40 and 10 years respectively.