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Question
A man is thrice as old as his son. Five years ago the man was four times as old as his son. Find their present ages.
Solution
Let the present age of the son be x years.
As the man is 3 times as old as his son, the present age of the man will be (3x) years.
5 years ago:
Son's age = (x − 5) years
Man's age = (3x − 5) years
According to the question:
(3x − 5) = 4(x − 5)
or, 3x − 5 = 4 × x − 4 × 5 [On expanding the brackets]
or, 3x − 5 = 4x − 20
or, 20 − 5 = 4x − 3x [Transposing 3x to the R.H.S. and 20 to the L.H.S.]
or, x = 15
∴ Present age of the son = 15 years
Present age of the man = 3x = 3 × 15
= 45 years
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