A father is three times as old as his son, and his daughter is 3 years younger
than the son. If the sum of their ages 3 years ago was 63 years, find the present age of the father.
pls answer asap.
Answers
Given:-
- A father is three times as old as his son
- His daughter is 3 years younger than his son.
To Find:-
- The present age of father.
Assumption:-
- Let us assume that the present age of son is x
- Present age of Father = 3x
- Present age of daughter = (x - 3)
Solution:-
3 years ago,
Age of Son = (x - 3) years
Age of father = (3x - 3) years
Age of daughter = x - 3 - 3 = (x - 6) years
ATQ,
Sum of their ages before 3 years was 63 years
Hence,
(x - 3) + (3x - 3) + (x - 6) = 63
= x - 3 + 3x - 3 + x - 6 = 63
=> 5x - 12 = 63
=> 5x = 63 + 12
=> 5x = 75
=> x = 75/5
=> x = 15
Now,
As we got the value of x, we can substitute it's value in the age of father to get the age of father.
Hence,
We assumed the present age of father to be 3x.
Substituting the value of x
Age of father = 3x = 3 × 15 = 45 years.
Therefore the present age of the father is 45 years.
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How did I solve?
Firstly we were told in the question that the age of father is three times the age of his son. So if we assume the age of son to be x then the age of father would be 3 times x i.e., 3x years. Also it is said that the age of the daughter is 3 less than the age of son. Hence the age of daughter would be (x - 3) years. After that we found their ages 3 years ago and found their sum, through which we got the value of x and after substituting the value of x in the age of father we assumed, we got the age of father.
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