If P + $$\frac{1}{Q}$$ = 1 and Q + $$\frac{1}{R}$$ = 1, then what is PQR?

Correct option is A

Given:

P + $$\frac{1}{Q}$$​ = 1 and Q +$$\frac{1}{R}$$​ = 1,

We are to find the value of P × Q × R

Solution:

$$\begin{aligned}&\text{} \\&P + \frac{1}{Q} = 1 \Rightarrow P = 1 - \frac{1}{Q} \\&Q + \frac{1}{R} = 1 \Rightarrow \frac{1}{R} = 1 - Q \Rightarrow R = \frac{1}{1 - Q} \\[10pt]&\text{Now, compute } P \times Q \times R: \\&P \times Q \times R = \left(1 - \frac{1}{Q} \right) \times Q \times \frac{1}{1 - Q} \\[10pt]&= (Q - 1) \times \frac{1}{1 - Q} \\[10pt]&= \frac{Q - 1}{1 - Q} = \frac{- (1 - Q)}{1 - Q} = -1\end{aligned}$$​

Correct Option: (A) -1