The average weight of P, Q and R is 45 kg. If the average weight of P and Q be 36.5 kg and that of Q and R be 52 kg, then what is the weight (in kgs) of Q?

Let weights of P,Q and R be $$p,q,r$$ kg respectively.

Average weight of P, Q and R = 45 kg

=> Sum of weights of P,Q and R = $$(p+q+r)=3\times45=135$$ kg -----------(i)

Average weight of P and Q = 36.5 kg

=> Sum of weights of P and Q = $$(p+q)=2\times36.5=73$$ kg ----------(ii)

Similarly, sum of weights of Q and R = $$(q+r)=2\times52=104$$ kg -----------(iii)

Adding equations (ii) and (iii),

=> $$p+2q+r=73+104=177$$ -----------(iv)

Subtracting equation (i) from (iv), 

=> $$q=177-135=42$$ kg

=> Ans - (A)