Question
In a family, the mother is 3 years younger than the father
and three times as old as the daughter. If their combined age is 84 years, how many years later will the father be twice as old as the daughter?Solution
ATQ,
Let the present age of the daughter and the mother be 'x' years and '3x' years, respectively.
Then, present age of the father = (3x + 3) years
So, x + 3x + (3x + 3) = 84
Or, 7x + 3 = 84
So, x = (84 - 3) ÷ 7 = 11
Present ages of the daughter and father are 11 years and 36 years, respectively.
For some 'y',
(11 + y) × 2 = (36 + y)
Or, 22 + 2y = 36 + y
So, y = 14
14 years hence from now, the father will be twice as old as the daughter.
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