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Q: The age of a father six years ago was six times the age of his daughter. Three years later the father will be thrice as old as his daughter. What is the present age of the daughter?
  • A. 15 years
  • B. 12 years
  • C. 17 years
  • D. 20 years
Correct Answer: Option B - Let the present age of father and daughter be x and y respectively. According to first condition, x – 6 = 6(y–6) x – 6 = 6y – 36 x – 6y = –30 -------(i) According to second condition, x + 3 = 3(y + 3) x + 3 = 3y + 9 x – 3y = 6 ------(ii) On solving equation (i) and (ii) x = 42, y = 12 Hence the present age of daughter (y) = 12 years.
B. Let the present age of father and daughter be x and y respectively. According to first condition, x – 6 = 6(y–6) x – 6 = 6y – 36 x – 6y = –30 -------(i) According to second condition, x + 3 = 3(y + 3) x + 3 = 3y + 9 x – 3y = 6 ------(ii) On solving equation (i) and (ii) x = 42, y = 12 Hence the present age of daughter (y) = 12 years.

Explanations:

Let the present age of father and daughter be x and y respectively. According to first condition, x – 6 = 6(y–6) x – 6 = 6y – 36 x – 6y = –30 -------(i) According to second condition, x + 3 = 3(y + 3) x + 3 = 3y + 9 x – 3y = 6 ------(ii) On solving equation (i) and (ii) x = 42, y = 12 Hence the present age of daughter (y) = 12 years.