A single discount equivalent to successive discounts of `30%,20%` and `10%` is

Options

A. `50%`
B. `51%`
C. `49.4%`
D. `49.6%`

Answer

To find the single discount equivalent to successive discounts of 30%, 20%, and 10%, we can follow these steps:

### Step 1: Assume a Mark Price
Let's assume the Mark Price (MP) of the item is ₹100. This simplifies our calculations.

### Step 2: Calculate the Selling Price after the First Discount
The first discount is 30%.
- Calculate the amount of the first discount:
\[ \text{First Discount} = 30\% \text{ of } 100 = \frac{30}{100} \times 100 = ₹30 \]
- Now, subtract this discount from the Mark Price:
\[ \text{Selling Price after First Discount} = 100 - 30 = ₹70 \]

### Step 3: Calculate the Selling Price after the Second Discount
The second discount is 20% on the new Selling Price (₹70).
- Calculate the amount of the second discount:
\[ \text{Second Discount} = 20\% \text{ of } 70 = \frac{20}{100} \times 70 = ₹14 \]
- Now, subtract this discount from the Selling Price after the first discount:
\[ \text{Selling Price after Second Discount} = 70 - 14 = ₹56 \]

### Step 4: Calculate the Selling Price after the Third Discount
The third discount is 10% on the new Selling Price (₹56).
- Calculate the amount of the third discount:
\[ \text{Third Discount} = 10\% \text{ of } 56 = \frac{10}{100} \times 56 = ₹5.60 \]
- Now, subtract this discount from the Selling Price after the second discount:
\[ \text{Selling Price after Third Discount} = 56 - 5.60 = ₹50.40 \]

### Step 5: Calculate the Total Discount
Now, we can calculate the total discount given from the original Mark Price:
\[ \text{Total Discount} = \text{Mark Price} - \text{Selling Price after Third Discount} = 100 - 50.40 = ₹49.60 \]

### Step 6: Calculate the Single Equivalent Discount
To find the single equivalent discount percentage, we use the formula:
\[ \text{Single Discount} = \left(\frac{\text{Total Discount}}{\text{Mark Price}}\right) \times 100 \]
Substituting the values:
\[ \text{Single Discount} = \left(\frac{49.60}{100}\right) \times 100 = 49.60\% \]

### Final Answer
The single discount equivalent to successive discounts of 30%, 20%, and 10% is **49.60%**.

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