Multiple choice

The average weight of five friends P, Q, R, S, and T is ( (x + 6) ) kg while the average weight of R and T is ( (x – 6) ) kg. If the weight of another person U is also added, then the average weight of all of them is reduced by 5 kg. Find the value of ‘x’ if the average weight of P, Q, S and U is 94.5 kg.

  1. 90

  2. 88

  3. 70

  4. 60
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A Correct answer
Explanation

Let P+Q+R+S+T = 5(x+6) = 5x+30. Given R+T = 2(x-6) = 2x-12, so P+Q+S = 3x+42. Adding U makes average reduce by 5: (5x+30+U)/6 = x+6-5 = x+1, so 5x+30+U = 6x+6, giving U = x-24. Also P+Q+S+U = 4×94.5 = 378. Substituting: (3x+42)+(x-24) = 378, so 4x+18 = 378, 4x = 360, x = 90.

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