Question
The sum of the present ages of 'P' and 'R' is 70 years.
'y' years ago from now, the age of 'R' was 40% more than that of 'P'. If '2y' years hence from now, the age of 'P' will be 20% less than that of 'R', determine the value of 'y'.Solution
Let the present age of R be 'x' years and present age of P be '70 - x' ATQ; (x - y) = 1.4 × (70 - x - y) Or, x - y = 98 - 1.4x - 1.4y Or, 2.4x + 0.4y = 98 Or, 6x + y = 245 So, y = 245 - 6x........ (I) Also, (x + 2y) × 0.8 = (70 - x + 2y) Or, 0.8x + 1.6y = 70 - x + 2y Or, 1.8x - 0.4y = 70 Or, y = 4.5x - 175 ........ (II) Using equation (I) and (II) , we have; 245 - 6x = 4.5x - 175 Or, 420 = 10.5x So, x = 40 So, y = 245 - (40 × 6) = 5
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