10 years ago, a woman was thrice the age of her daughter. Two years later her daughter’s age will be 30 more than the age of the mother. What are the present ages of the woman and the daughter?

10 years ago, a woman was thrice the age of her daughter. Two years later her daughter’s age will be 30 more than the age of the mother. What are the present ages of the woman and the daughter? Correct Answer 55 years, 25 years

Let the present ages of mother be x years and daughter be y years. 10 years ago, Age of mother = x-10 years Age of daughter = y-10 years Age of mother = 3(age of daughter) x-10=3(y-10) x-10=3y-30 x-3y+20=0 x=3y-20     (1) Two years later, Age of mother = x+2 years Age of daughter = y+2 years Age of mother will be 30 more than the age of daughter x+2=y+2+30 x=y+30     (2) From (1) and (2), we get, y+30=3y-20 30+20=3y-y 50=2y y=25 Substituting y=25 in equation (1) we get, x=3(25)-20 x=55 The present age of mother is 55 years and that of daughter is 25 years.
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