A discount series of p% and q% on an invoice is the same as a single discount of -

Answer: Option D

Let marked price be Rs. 100
Then,
S.P. = (100 - q)% of (100 - p)% of Rs. 100
$$\begin{array}{rl}& =\text{Rs}\text{.}\left[\frac{100-\text{q}}{100}\times \frac{100-\text{p}}{100}\times 100\right]\\ & =\text{Rs}.\left[\frac{\left(100-\text{q}\right)\left(100-\text{p}\right)}{100}\right]\\ & \therefore \text{Single discount }\\ & =\left\{100-\left[\frac{\left(100-\text{q}\right)\left(100-\text{p}\right)}{100}\right]\right\}\%\\ & =\left(\text{p}+\text{q}-\frac{\text{pq}}{100}\right)\%\end{array}$$