Six years ago a man was three times as old as his son. In 6 year’s time, he will be twice as old as his son.
Six years ago a man was three times as old as his son. In 6 year’s time, he will be twice as old as his son. Then their present ages are
A) 30, 15
B) 40, 20
C) 42, 18
D) 41, 19
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Correct option is (C) 42, 18
Let present age of son be x years and
present age of father be y years.
Then according to given conditions, we get
y - 6 = 3 (x - 6)
\(\Rightarrow\) y = 3x - 12 ____________(1)
and y + 6 = 2 (x+6)
\(\Rightarrow\) 2x+12 = y+6
\(\Rightarrow\) 2x - y + 6 = 0 ____________(2)
From (1) & (2), we get
2x - (3x - 12) + 6 = 0
\(\Rightarrow\) 2x - 3x + 12 + 6 = 0
\(\Rightarrow\) x = 18
\(\therefore\) y = 3x - 12
= 54 - 12 = 45 (From (1))
Hence, their present ages are 18 & 42 years.
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