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

Let the initial marked price of the item be $\text{₹ }100$.
* After the first discount of $10\%$, the price becomes:

$$100\times \left(1-\frac{10}{100}\right)=100\times 0.9=\text{₹ }90$$

* After the second discount of $20\%$, the price becomes:

$$90\times \left(1-\frac{20}{100}\right)=90\times 0.8=\text{₹ }72$$

* After the third discount of $20\%$, the final price becomes:

$$72\times \left(1-\frac{20}{100}\right)=72\times 0.8=\text{₹ }57.6$$

The total effective discount offered is:

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