The single discount which is equivalent to successive discount of 25%, 20% and 10% is

Options

A. `55%`
B. `54%`
C. `46%`
D. `45%`

Answer

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

### Step 1: Assume the MRP
Assume the Maximum Retail Price (MRP) of the item is ₹100.

### Step 2: Apply the first discount
The first discount is 25%. Calculate the price after this discount:
- Discount amount = 25% of ₹100 = ₹25
- Price after first discount = ₹100 - ₹25 = ₹75

### Step 3: Apply the second discount
The second discount is 20%. Calculate the price after this discount:
- Discount amount = 20% of ₹75 = ₹15
- Price after second discount = ₹75 - ₹15 = ₹60

### Step 4: Apply the third discount
The third discount is 10%. Calculate the price after this discount:
- Discount amount = 10% of ₹60 = ₹6
- Price after third discount = ₹60 - ₹6 = ₹54

### Step 5: Calculate the total discount
Now, we need to find out how much discount was given from the original MRP of ₹100 to the final price of ₹54:
- Total discount = ₹100 - ₹54 = ₹46

### Step 6: Calculate the equivalent single discount percentage
To find the equivalent single discount percentage:
- Equivalent discount percentage = (Total discount / Original Price) × 100
- Equivalent discount percentage = (₹46 / ₹100) × 100 = 46%

Thus, the single discount which is equivalent to successive discounts of 25%, 20%, and 10% is **46%**.

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