Five years ago a man was seven times as old as his son. Five year hence, the father will be three times as old as his son. Find their present ages?

 ANSWERE = 

call the present age of the father "x".


Five years ago, the father was x - 5 years old, and his son was x / 7 - 5 years old.


According to the first statement, five years ago the father was seven times as old as his son:


x - 5 = 7 * (x / 7 - 5)


Expanding and simplifying the right-hand side:


x - 5 = 7 * (x / 7) - 35


x - 5 = x - 35


Solving for x:


x = 40


So the present age of the father is 40 years and the present age of the son is 40 / 7 = 5.71 years old (rounded to the nearest year, the son is 6 years old)

[2/11, 10:37 AM] vbajrang54: Let's verify that in five years the father will indeed be three times as old as his son:


In five years, the father will be 40 + 5 = 45 years old, and the son will be 6 + 5 = 11 years old.


So in five years, the father will be 45 / 11 = 4.09 times as old as his son (rounded to the nearest tenth, the father will be 4 times as old as his son). This confirms that the ages we have calculated are correct.

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