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Answer :
Final answer:
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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