Question
Pintu' is father of 'Qasim'. '2x' years ago from now,
the age of 'Pintu' was four times the age of 'Qasim'. While, '2x' years hence from now, age of 'Pintu' will be twice the age of 'Qasim'. If sum of ages of 'Pintu' and 'Qasim', '0.5x' years hence from now will be 90 years, then find the average of present ages of 'Pintu' and 'Qasim'.Solution
ATQ, Let the present ages of 'Pintu' and 'Qasim' be 'a' years and 'b' years, respectively. ATQ; (a - 2x) = 4 X (b - 2x) Or, a - 2x = 4b - 8x Or, a = 4b - 6x ...... (I) And, (a + 2x) = 2 X (b + 2x) Or, a + 2x = 2b + 4x Or, a = 2b + 2x ....... (II) Using equation (I) and (II) , we have; 4b - 6x = 2b + 2x Or, 2b = 8x So, b = 4x .... (III) And a = 2b + 0.5 So, a = 2.5b ..... (IV) (a + 0.5x + b + 0.5x) = 90 Using equation (III) and (IV) , we have; (2.5 X 4x + 0.5x + 4x + 0.5x) = 90 10x + x + 4x = 90 Or, 15x = 90 So, x = 6 So, b = 4x = 4 X 6 = 24 and a = 2.5b = 2.5 X 24 = 60 So, present age of 'Pintu' = 'a' = 60 years And present age of 'Qasim' = b = 24 years So, required average = (60 + 24) ÷ 2 = 42 years
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