A single equivalent discount equivalent to three successive discounts of 10% , 16% and 25% is equal to:

Options

A. `42%`
B. `46.5%`
C. `41%`
D. `43.3%`

Answer

To find the single equivalent discount for three successive discounts of 10%, 16%, and 25%, we can follow these steps:

### Step 1: Understand the Discounts
We start with an initial market price (MP) of 100. The discounts are applied successively, which means each discount is applied to the price after the previous discount has been deducted.

### Step 2: Calculate the Selling Price after Each Discount
1. **First Discount (10%)**:
- After applying the first discount of 10%, the selling price (SP1) becomes:
\[ SP1 = MP \times \left(1 - \frac{10}{100}\right) = 100 \times 0.90 = 90 \]

2. **Second Discount (16%)**:
- Now apply the second discount of 16% on the new selling price (SP1):
\[ SP2 = SP1 \times \left(1 - \frac{16}{100}\right) = 90 \times 0.84 = 75.6 \]

3. **Third Discount (25%)**:
- Finally, apply the third discount of 25% on the new selling price (SP2):
\[ SP3 = SP2 \times \left(1 - \frac{25}{100}\right) = 75.6 \times 0.75 = 56.7 \]

### Step 3: Calculate the Equivalent Discount
Now we have the final selling price (SP3) of 56.7. To find the equivalent discount percentage, we use the formula:
\[ \text{Equivalent Discount} = \frac{MP - SP3}{MP} \times 100 \]
Substituting the values:
\[ \text{Equivalent Discount} = \frac{100 - 56.7}{100} \times 100 = \frac{43.3}{100} \times 100 = 43.3\% \]

### Conclusion
The single equivalent discount for the three successive discounts of 10%, 16%, and 25% is **43.3%**.