Successive discounts of $p\%$ and $q\%$ on an invoice is the same as a single discount of
Solution
✅ Correct Option: 1
Take the original price as 100, since we want the answer as a percentage. After the first discount of $p\%$, the price left is $100-p$ The second discount of $q\%$ applies to this reduced price: $(100-p)-\dfrac{q}{100}(100-p)$ $=(100-p)\left(1-\dfrac{q}{100}\right)$ $=100-p-q+\dfrac{pq}{100}$ $\text{Total discount}=\text{starting price}-\text{final price}$ $=100-\left(100-p-q+\dfrac{pq}{100}\right)$ $=p+q-\dfrac{pq}{100}$ Since we started from 100, this number is already the percentage: $\left[p+q-\dfrac{pq}{100}\right]\%$ The minus sign makes sense, because the second discount is taken on a smaller price, so you save a little less than $p+q$.