Question

The average weight of there boys P, Q, & R is 54$\dfrac{1}{3}$ kg while the average weight of three boys Q, S, & T is 53 kg what is the average weight of P, Q, R, S, & T ?
A. 52.4kg
B. 53.2kg
C. 53.8kg
D. Data inadequate

Answer 1

Hint:- We know the average weight of three boys P, Q & R. So we can get the total weight of three boys P, Q & R. Similarly we can get the total weight of three boys Q, S & T from this average weight we only have this data. We will be able to find the average weight of P, Q, R, S & T from this data.

Complete step-by-step answer:
Given :-
Average weight of three boys
  P,Q & R = 54$\dfrac{1}{3}$ kg
  $ \Rightarrow $ $\dfrac{{{\text{Total}}\,{\text{weight}}\,{\text{of}}\,{\text{three}}\,{\text{boys}}\,{\text{P,Q,R }}\,{\text{}}}}{{\text{3}}}$ = $\dfrac{{163}}{3}$
  $ \Rightarrow $ Total weight of three boys P, Q & R = 163 kg
  $ \Rightarrow $ P+Q+R $ \to $ ( i )
         = 163 kg

Also given that:
Average that three boys Q, S ,T
 $ \Rightarrow $ $\dfrac{{{\text{Total}}\,{\text{weight}}\,{\text{of}}\,{\text{three}}\,{\text{boys}}\,{\text{Q,}}\,{\text{S}}\,{\text{\& }}\,{\text{T}}}}{{\text{3}}}{\text{ = 53kg}}$
 $ \Rightarrow $ Total weight of three boys Q, S & T =159 kg
 $ \Rightarrow $ Q+S+T = 159 $ \to $ (ii)
We will add both (i) & (ii)
$\therefore $ i.e. P+Q+R = 163 $ \to $ (i)
                    Q+S+T = 159 $ \to $
               $(i)\, + \,(ii)$ gives
 P + 2Q + S + R + T = 322
We need to find average weight of P, Q, R, S, T i.e.
  we need to find
  $\dfrac{{{\text{P + 2Q + S + R + T}}}}{{\text{5}}}$
But we know P + 2Q + R + S + T so we need to know the separate weight of to find average weight of
P, Q, R, S & T.
$\therefore $ Therefore data given is insufficient.
Correct option (D). Data inadequate.

Note:- We can not find a solution to this question as data given is insufficient.
We need to know the weight of Q to calculate the average weight of P, Q, R, S & T.