Five years later, the father’s age will be three times the age of his son. Five years ago, a father was seven times as old as his son. Find their present ages.

Question

Vedantu Content Team · Accepted Answer

Hint: Start by taking the present age of father and son to be x and y respectively. Then according to the conditions given in the question, form the equation and solve the equation by performing arithmetic operations.

Complete step-by-step answer:
Let x be the present age of father and y be the present age of son.
According to the question, after 5 years father’s age will be (x+5) and son’s age will be (y+5), then
x+5 = 3(y+5)
x-3y-10 = 0 …..(1)
According to the question, another condition is given such that,
Five years ago, the age of the father was (x-5) and son’s age was (y-5), so according to the condition,
(x-5) = 7(y-5)
x-7y+30 = 0 …..(2)
Now we will solve (1) and (2), by subtracting (1) from (2),
$ - 3y + 7y - 10 - 30 = 0$
$ \Rightarrow y = 10$
We have found the age of son, now to find the age of father we are going to put the value of y in one of the equations,
Let us put y = 10 in (1),
$x - 3\left( {10} \right) - 10 = 0$
$ \Rightarrow x = 40$
Therefore, father’s present age is 40 and son’s present age is 10.

Note: In age problems, if we have one person we can easily solve it by taking one variable and forming an equation using the condition given. In case there are 2 people, we assign one variable to one of the people and the second variable to the other one and then form equations using the conditions given in the question.

Five years later, the father’s age will be three times the age of his son. Five years ago, a father was seven times as old as his son. Find their present ages.

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Five years later, the father’s age will be three times the age of his son. Five years ago, a father was seven times as old as his son. Find their present ages.

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