Ten years ago, a father was 4 times as old as his son. Ten years hence, the father will be twice as old as his son. What are their present ages?OptionsFather: 40 years, Son: 10 yearsFather: 45 years, Son: 15 yearsFather: 50 years, Son: 20 yearsFather: 60 years, Son: 30 years
Question
Ten years ago, a father was 4 times as old as his son. Ten years hence, the father will be twice as old as his son. What are their present ages?OptionsFather: 40 years, Son: 10 yearsFather: 45 years, Son: 15 yearsFather: 50 years, Son: 20 yearsFather: 60 years, Son: 30 years
Solution
Let's denote the present age of the father as F and the present age of the son as S.
From the problem, we have two equations:
-
F - 10 = 4 * (S - 10) (Ten years ago, the father was four times as old as his son)
-
F + 10 = 2 * (S + 10) (In ten years, the father will be twice as old as his son)
We can solve these two equations to find the values of F and S.
From the first equation, we can express F in terms of S: F = 4S - 30
Substitute F in the second equation: 4S - 30 + 10 = 2S + 20
Simplify the equation: 2S = 40
So, S = 20
Substitute S = 20 in the equation F = 4S - 30, we get F = 50
So, the father is 50 years old and the son is 20 years old. Therefore, the correct option is "Father: 50 years, Son: 20 years".
Similar Questions
After five years the age of a father will be thrice the age of his son whereas five years ago, he was seven times old as his son was.What is father's present age?30 years40 years50 yearsNone of these
answerAge of the father is twice that of the elder son. Ten years hence the age of the father will be three times that of the younger son. If the difference of the ages of the two sons is 15 years, the age (in years) of the father is?Options50605570
2 years ago, the father's age was 6 times of his son's age. 6 years hence the ratio between the ages of father and thif son becomes 10:3. What is the father's present age?A40 YearsB42 YearsC44 YearsD48 Years
The age of a man is 3 times that of his son .15 years ago, the man was 9 times as old as his son. What will be the age of the man after 10 years?
The sum of the ages of a father and his son is 45 years. If 5 years ago, the father was 4 times as old as his son, what is the present age of the son?a.9b.11c.7d.5
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.