There are three numbers 'u', 'v' and 'w' (u < v < w) such that 'v' is equal to the average of 'u' and 'w'. 80% of 'w' is equal to 'u' and the difference between 'v' and 'w' is 20. Find the sum of all three numbers.
ATQ, 'v' = (1/2) × (u + w) Or, 2v = u + w And, 0.8w = 'u' Or, w = 5:4 Let 'w' = '5h' and 'u' = '4h' So, 2v = 4h + 5h Or, 'v' = (9h/2) Now, w - v = 20 Or, 5h - (9h/2) = 20 Or, (h/2) = 20 Or, 'h' = 40 Required sum = 4h + {(9/2) × 40} + (5 × 40) = 160 + 180 + 200 = 540
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