Two years ago, sumitra was five times as old as her daughter, and eight years hence , the mother will be thrice old as her daughter. Find thier present ages.

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Solution

$Let the age of daughter 2 years ago = x yrs Then the age of Sumitra, 2 yrs ago = 5 x yrs Present age of daughter = (x + 2) yrs Present age of Sumitra = (5 x + 2) yrs After 8 years : Daughter' s age = (x + 10) yrs Sumitra' s age = (5 x + 10) yrs According to question, 5 x + 10 = 3 (x + 10) \Rightarrow 5 x + 10 = 3 x + 30 \Rightarrow 5 x - 3 x = 30 - 10 \Rightarrow 2 x = 20 \Rightarrow x = 10 So, present age of daughter = x + 2 = 10 + 2 = 12 yrs present age of Sumitra = 5 x + 2 = 5 \times 10 + 2 = 50 + 2 = 52 yrs$

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