Step 1: Understand Successive Discounts

When two successive discounts $a\%$ and $b\%$ are applied to a marked price, the net single equivalent discount $D_{eq}$ is calculated using the formula $D_{eq} = \left(a + b - \frac{a \times b}{100}\right)\%$

$D_{eq} = \left(a + b - \frac{a \times b}{100}\right)\%$

Step 2: Test Option B ($20\%$ and $80\%$)

Substitute $a = 20$ and $b = 80$ into the formula: $D_{eq} = 20 + 80 - \frac{20 \times 80}{100} = 100 - \frac{1600}{100} = 100 - 16 = 84\%$

$20 + 80 - \frac{20 \times 80}{100} = 84\%$

Step 3: Alternative Multiplier Method

Alternatively, multiplying the remaining price fractions gives: $(1 - 0.20) \times (1 - 0.80) = 0.80 \times 0.20 = 0.16$ Thus, the final price is $16\%$ of the original, meaning the total discount is $100\% - 16\% = 84\%$.

$0.80 \times 0.20 = 0.16 \implies 84\% \text{ discount}$