The single discount, which is equal to three successive discounts of 10%, 20% and 25%, is :

Question

Accepted Answer

To determine the single discount equivalent to three successive discounts of 10%, 20%, and 25%, we need to calculate the cumulative effect of these discounts on the original price.

Let's assume the original price is 100 units.

1. **First Discount (10%)**:  
   - After a 10% discount, the price becomes 90 units.  
   (Calculation: 100 - 10% of 100 = 100 - 10 = 90)

2. **Second Discount (20%)**:  
   - After a 20% discount on the new price (90 units), the price becomes 72 units.  
   (Calculation: 90 - 20% of 90 = 90 - 18 = 72)

3. **Third Discount (25%)**:  
   - After a 25% discount on the new price (72 units), the price becomes 54 units.  
   (Calculation: 72 - 25% of 72 = 72 - 18 = 54)

Now, the final price after all three successive discounts is 54 units. The original price was 100 units.

To find the single equivalent discount, we calculate the total reduction from the original price:

- Reduction = Original Price - Final Price = 100 - 54 = 46 units

The single discount percentage is then calculated as:

- Single Discount Percentage = (Reduction / Original Price) * 100  
  = (46 / 100) * 100  
  = 46%

Therefore, the single discount equivalent to the three successive discounts is 46%, which corresponds to Option 2.

**Explanation for Incorrect Options:**

1. **Option 1 (49.60%)**:  
   This option is incorrect because the cumulative effect of the discounts does not result in a 49.60% reduction. The calculations show a 46% reduction.

2. **Option 3 (50.40%)**:  
   This option is incorrect as the cumulative discounts do not lead to a 50.40% reduction. The correct calculation results in a 46% reduction.

3. **Option 4 (52%)**:  
   This option is incorrect because the total reduction from the original price is not 52%. The correct single discount is 46%.

In conclusion, the correct single discount equivalent to the three successive discounts of 10%, 20%, and 25% is 46%, which is why Option 2 is the correct answer.