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

Explanation:-

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