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Question
A man is 4 times as old as his son. After 16 years he will be only twice as old as his son. Find their present ages.
Solution
Let the present age of the son be x years.
As the man is 4 times as old as his son, the present age of the man will be (4x) years.
After 16 years:
Son's age = (x + 16) years
Man's age = (4x + 16) years
According to the question:
(4x + 16) = 2(x + 16)
or, 4x + 16 = 2 × x + 2 × 16 [On expanding the brackets]
or, 4x + 16 = 2x + 32
or, 4x − 2x = 32 − 16 [Transposing 16 to the R.H.S. and 2x to the L.H.S.]
or, 2x = 16
or, `(2x)/2=16/2` [Dividing both the sides by 2]
or, x = 8
∴ Present age of the son = 8 years
Present age of the man = 4x = 4 × 8
= 32 years
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