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The sum of the ages of a daughter and her mother is 56 years. After 4 years, the age of the mother will be three times that of the daughter. At present their ages are ?

The sum of the ages of a daughter and her mother is 56 years. After 4 years, the age of the mother will be three times that of the daughter. At present their ages are ? Correct Answer 12 years, 44 years

Let daughter's age be $$x$$ years.
Then, mother's age = (56 $$-\, x\,$$) years
$$\eqalign{ & \left( {56 - x} \right)+4 = 3\left( {x + 4} \right) \cr & \Rightarrow 60 - x = 3x + 12 \cr & \Rightarrow 4x = 48 \cr & \Rightarrow x = 12 \cr} $$
∴ Daughter's age = 12 years
And the mother's age = (56 $$-$$ 12) = 44 years

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