A $20\%$ discount is offered on an item. By applying a promo code, the customer wins $15\%$ cashback. What is the effective discount?

Let the marked price of the item be \ 100$.First,adiscountof$ 20\%$isgiven:$\text{Price after initial discount} = 100 - \left(\frac{20}{100} \times 100\right) = \ 80
Then, a $15\%$ cashback is applied to this reduced price:
\text{Cashback amount} = \frac{15}{100} \times 80 = \$12$$Calculatethefinaleffectivepricepaidbythecustomer:$\text{Effective Price} = 80 - 12 = \ 68
$$Calculatethetotaleffectivediscount:$$
\text{Total Discount} = 100 - 68 = \$32$ $
$$\text{Effective Discount Percentage}=\left(\frac{32}{100}\right)\times 100\%=32\%$$
Alternatively, using the successive discount formula:
$$\text{Net Discount}=x+y-\frac{xy}{100}$$
$$\text{Net Discount}=20+15-\frac{20\times 15}{100}=35-3=32\%$$