Question

5 year ago a man was 7 times as old as his son. After 5 years he will be thrice as old as his son . Find their present ages.

Answer 1

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Answer 2

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Let the present age of man and his son be X and Y years.




Before 5 years age of man = ( X - 5 ) years.


Before 5 years age of his son = ( Y - 5) years.



According to question,




( X - 5) = 7 ( Y - 5)

X - 5 = 7Y - 35


X - 7Y = -35+5



X - 7Y = -30 ---------(1)


After 5 years age of man = ( X + 5) years.



After 5 years age of son = ( Y + 5) years.



According to question,



( X + 5) = 3 ( Y + 5)



X + 5 = 3Y + 15




X - 3Y = 15 - 5



X - 3Y = 10 ----------(2)



From equation (1) we get,




X - 7Y = -30



X = (-30 + 7Y ) ---------(3)


Putting the value of X in equation (2)



X - 3Y = 10



-30 + 7Y - 3Y = 10



4Y = 10 + 30



Y = 40/4 = 10


Putting the value of Y in equation (3)



X = -30 + 7Y = -30 + 7 × 10 = -30 + 70



X = 40 years.


Present age of man = X = 40 years


And,


Present age of son = Y = 10 years.



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