Five years ago a man was seven times older than his son. Five years hence, the father will be three times as old as his son. Find their present ages.
Answers
Given :
- Five years ago, a man was seven times older than his son.
- Five years hence, the father will be three times as old as his son.
To find :
- Present age of Man and his son?
Solution :
☯ Let 5 years ago the age of son be x years and age of father be 7x years.
Therefore,
- Present age of son = (x + 5) years
- Present age of Man = (7x + 5) years
Now,
★ According to the Question:
- Five years hence, the father will be three times as old as his son.
Their ages after 5 years,
- Age of son = (x + 5) + 5 = (x + 10) years
- Age of Man = (7x + 5) + 5 = (7x + 10) years
Therefore,
➯ 7x + 10 = 3(x + 10)
➯ 7x + 10 = 3x + 30
➯ 7x - 3x = 30 - 10
➯ 4x = 20
➯ x = 20/4
➯ x = 5
Hence,
- The Present age of son, (x + 5) = 5 + 5 = 10 years
- The Present age of man or his father, (7x + 10) = 35 + 5 = 40 years
∴ Present age of man and his son is 40 years and 10 years respectively.
Answer:
Given :-
- Five years ago a man was seven times older than his son. Five years hence, the father will be three times as old as his son.
To Find :-
- What is their present ages.
Solution :-
★ Five years ago,
» Age of son be x
» And, the age of his father will be 7x
Hence,
Present age of son = x + 5
And, the present age of his father = 7x + 5
★ 5 years later,
» Age of son = x + 5 + 5 = x + 10
» And, the age of his father = 7x + 5 + 5 = 7x + 10
According to the question,
⇒ 7x + 10 = 3(x + 10)
⇒ 7x + 10 = 3x + 30
⇒ 7x - 3x = 30 - 10
⇒ 4x = 20
⇒ x = 20 ÷ 4
➠ x = 5
Hence, their present ages will be,
✧ Present age of son = x + 5 = 5 + 5 = 10 years
✧ Present age of his father = 7x + 5 = 7(5) + 5 = 35 + 5 = 40 years
∴ Present age of son is 10 years and present age of his father will be 40 years .
Let's Verify :-
↣ 7x + 10 = 3(x + 10)
Put x = 5 we get,
↣ 7(5) + 10 = 3(5 + 10)
↣ 35 + 10 = 15 + 30
➠ 45 = 45
➦ LHS = RHS
Hence, Verified ✔