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.
Answer
Verified
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.
×
Sorry!, This page is not available for now to bookmark.