The successive discount of 25%, 20% and 10% is equivelant to a single discount of:

Options

A. 0.46
B. 0.48
C. 0.54
D. 0.44

Answer

To find the equivalent single discount for successive discounts of 25%, 20%, and 10%, we can follow these steps:

### Step 1: Combine the first two discounts (25% and 20%)
We will use the formula for combining two successive discounts:
\[ \text{Single Discount} = X + Y - \left(\frac{X \times Y}{100}\right) \]
where \(X\) is the first discount (25%) and \(Y\) is the second discount (20%).

Substituting the values:
\[ \text{Single Discount} = 25 + 20 - \left(\frac{25 \times 20}{100}\right) \]

### Step 2: Calculate the product of the two discounts
Calculate \(25 \times 20\):
\[ 25 \times 20 = 500 \]
Now, divide by 100:
\[ \frac{500}{100} = 5 \]

### Step 3: Substitute back into the formula
Now substitute back into the formula:
\[ \text{Single Discount} = 25 + 20 - 5 \]
\[ \text{Single Discount} = 45 \]

### Step 4: Combine the result with the third discount (10%)
Now we need to combine this result (45%) with the third discount (10%) using the same formula:
\[ \text{Final Single Discount} = 45 + 10 - \left(\frac{45 \times 10}{100}\right) \]

### Step 5: Calculate the product of 45 and 10
Calculate \(45 \times 10\):
\[ 45 \times 10 = 450 \]
Now, divide by 100:
\[ \frac{450}{100} = 4.5 \]

### Step 6: Substitute back into the formula
Now substitute back into the formula:
\[ \text{Final Single Discount} = 45 + 10 - 4.5 \]
\[ \text{Final Single Discount} = 55.5 \]

### Conclusion
The equivalent single discount of successive discounts of 25%, 20%, and 10% is **55.5%**.

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