Question

The average weight of 3 person P, Q, R is 84 kg. Another person who is S joins the group and now the present average of the group 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.​

Answer 1

Answer:

76.75

Step-by-step explanation:

weight of P,Q,R each = 84

avg weight of P,Q,R,S= 80

weight of S = 80*4 - 84*3

= 68kg

Now weight of T = 68+3= 71kg (given in question)

avg weight of Q,R,S,T= (84+84+68+71)/4

=307/4

=76.75 kg

Answer 2

Answer:

weight of P = 79 kg

Step-by-step explanation:

Given data:

The average weight of 3 persons P, Q, R = 84 kg

after joining S average weight of P, Q, R, S = 80 kg

weight of T is 3 more than S weight  

after replacing T with P, average weight of Q, R, S, T = 78 kg

here we need to find weight of P  

From given data  

average weight of P, Q, R = $\frac{ P+Q+R}{3} = 84$  

         ⇒ P+Q+R = 84×3 = 252

         ⇒ P+Q+R = 252 kg _(1)  

after joining S average weight of P, Q, R, S = 80 kg

         ⇒ $\frac{P+Q+R+S }{4} = 80$  

         ⇒ P+Q+R+S = 320 kg _(2)

         ⇒ 252 + S = 320     [ from (1) ]

         ⇒  S = 68 kg

weight of T = 3 kg more than S

weight of T = 68+3 = 71 kg

After replacing P average weight of Q, R, S, T = 78 kg

        ⇒ $\frac{T+Q+R+S }{4} = 78$  

        ⇒ T+Q+R+S = 78×4  

        ⇒ T+Q+R+S = 312 kg

        ⇒ 71 +Q+R+S = 312 kg

                  Q+R+S = 312 - 71 = 241 kg  

                   Q+R+S = 241 kg _(3)

substitute (3) in (2)

    (2) =  P+Q+R+S = 320 kg  

             P + 241  = 320

             P = 79 kg