If aq - r = br - p = cp - q , find the value of pa + qb + rc is?

Answer: Option A

$$\begin{array}{rl}& \text{Let }\frac{a}{q-r}=\frac{b}{r-p}=\frac{c}{p-q}=k\\ & \frac{a}{q-r}=k\left(\text{On multiplying by }p\right)\\ & pa=k\left(pq-pr\right)......(i)\\ & \text{In the same way we can write}\\ & \text{qb = k}\left(qr-qp\right)........(ii)\\ & \text{And }rc=k\left(rp-rp\right).....iii)\\ & \text{On adding equation (i), (ii) and (iii) }\\ & pa+qb+rc\\ & =k\left(pq-pr+qr-qp+rp-rq\right)\\ & =0\end{array}$$