The successive discounts of 12%, 20%, and 25% are equivalent to a single discount of:

1. 52.2%
2. 49.5%
3. 47.2%
4. 57.0%

To find the single equivalent discount for successive discounts of 12%, 20%, and 25%, we need to apply each discount one after the other on an initial price, and then calculate the overall discount.
Let's assume the initial price of an item is $100.

Apply the first discount of 12%:
A 12% discount on $100 is $100 \times \frac{12}{100} = $12.
The new price after the first discount = $100 - $12 = $88.

Apply the second discount of 20%:
A 20% discount on $88 is $88 \times \frac{20}{100} = $17.60.
The new price after the second discount = $88 - $17.60 = $70.40.

Apply the third discount of 25%:
A 25% discount on $70.40 is $70.40 \times \frac{25}{100} = $17.60.
The new price after the third discount = $70.40 - $17.60 = $52.80.


The final price after all successive discounts is $52.80. This means that the customer pays $52.80 out of the original $100.
To find the single equivalent discount, we calculate the amount saved:
Savings = $100 - $52.80 = $47.20.
Now, calculate the equivalent discount percentage:
Equivalent discount percentage = \left(\frac{47.20}{100}\right) \times 100 = 47.2%
Therefore, the single equivalent discount is 47.2% , which corresponds to option 3.

Answered by IsabellaRoseDavis | 2025-07-06