Find the single equivalent discount percentage corresponding to three successive discounts of $10\%$, $20\%$, and $20\%$.

Let the initial Marked Price (MP) of the article be $\text{₹ }100$.
1. After the first discount of $10\%$:

$$\text{Price}=100-\left(100\times \frac{10}{100}\right)=\text{₹ }90$$

2. After the second successive discount of $20\%$:

$$\text{Price}=90-\left(90\times \frac{20}{100}\right)=90-18=\text{₹ }72$$

3. After the third successive discount of $20\%$:

$$\text{Final Selling Price (SP)}=72-\left(72\times \frac{20}{100}\right)=72-14.4=\text{₹ }57.6$$

Total equivalent discount offered:

$$\text{Total Discount}=\text{Marked Price}-\text{Selling Price}$$

$$\text{Total Discount}=100-57.6=42.4\%$$

Alternative Method using successive percentage formula $a+b-\frac{ab}{100}$:
First two discounts ($10\%$ and $20\%$):

$${\text{Equivalent Discount}}_1=10+20-\frac{10\times 20}{100}=30-2=28\%$$

Now combine $28\%$ with the remaining $20\%$ discount:

$$\text{Total Equivalent Discount}=28+20-\frac{28\times 20}{100}=48-5.6=42.4\%$$