P, Q, R, S and T are five persons. The weight of P, Q and R is 80%, 102% and 84% respectively of the average weight of all five. The ratio of weight of S and T is 5:8. The difference between the weight of S and T is 67.5 kg. What is the average weight of all the five persons?
Let the average weight of all five = 100x So, weight of P = 80x, Q = 102x and R = 84x Let the weight of S = a and that of T = b =>(80x + 102x + 84x + a + b)/5 = 100x => a + b = 234x => a : b = 5:8 → a = (5/13) × 234 = 90x → b = (8/13) × 234 = 144x Difference = 144x – 90x = 54x => 54x = 67.5 => x = (67.5/54) = 1.25 Average weight of all the five persons = 100 × 1.25 = 125 kg
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