In a queue P is eighteenth from the front while Q is sixteenth from the back. If R is twentieth from front and is exactly in the middle of P and Q, then how many persons are there in the queue?

37

we know,

(position of P from Left + position of Q from Left)/2 = middle position of R from Left

(18 + Q)/2 = 20 

18 + Q = 40

therefore, 

position of Q from Left is 22

and we know,

Total = Left Rank of Q + Right Rank of Q - 1

Total = 22 + 16 - 1

Total = 37