The average weight of three people, P, Q, and R, is 84 kg. Another person, S, joins the group, and the new average weight becomes 80 kg. If another person, T, whose weight is 3 kg more than that of S, replaces P, then the average weight of Q, R, S, and T becomes 78 kg. Find the weight of P.

The weight of person P is found by doing a series of calculations involving the given averages, the total numbers in each group and the known weights of S and T. The final calculation reveals that P weighs 8 kg.

Explanation:

We are given that the average weight of P, Q, and R is 84 kg which means the total weight of P, Q, and R is 84 * 3 = 252 kg.

When S is added into the group, the average weight becomes 80 kg, which implies the total weight is 80*4 = 320 kg. Hence the weight of S is calculated as 320 - 252 = 68 kg.

It is given that person T, whose weight is 3 kg more than S, replace P. So, the weight of T is 68+3 = 71 kg. When P is replaced with T, the new average of Q, R, S, T = 78 kg, implying the total weight is 78*4=312 kg.

To find the weight of P, calculate the weight of P, Q, R and subtract the weight of Q, R, S, and T. So, the weight of P = 252 (P+Q+R) - (weight of Q+R+S) = 252 - 312 + 68 (S weight) = 8 kg.

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