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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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