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:
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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:
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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
Age of Father = 40 Years
Age of Daughter = 10 Years
Given Terms:
Need To Find:
Solution: Let the present age of father be x years and daughter be y years.
Five years ago their ages were
Five years hence their ages would be
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.