Six years ago a man was three times as old as his son. In 6 year’s t

1.	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
Answer» 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. Correct option is C) 42, 18

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

Answer»

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.

Correct option is C) 42, 18