An item was sold after giving two successive discount of `20%` and `10%` respectively, If the item was sold for₹ 468. The marked price of that item is :

Options

A. ₹ 600
B. ₹ 500
C. ₹ 575
D. ₹ 650

Answer

To find the marked price of an item sold after giving two successive discounts of 20% and 10%, we can follow these steps:

### Step 1: Understand the Discounts
The item is sold after applying two successive discounts:
1. First discount = 20%
2. Second discount = 10%

### Step 2: Represent the Marked Price
Let the marked price of the item be denoted as \( MP \).

### Step 3: Calculate the Selling Price after the First Discount
After applying the first discount of 20%, the selling price becomes:
\[ SP_1 = MP - (20\% \text{ of } MP) = MP \times (1 - 0.20) = MP \times 0.80 \]

### Step 4: Calculate the Selling Price after the Second Discount
Now, applying the second discount of 10% on the price after the first discount:
\[ SP_2 = SP_1 - (10\% \text{ of } SP_1) = SP_1 \times (1 - 0.10) = SP_1 \times 0.90 \]
Substituting \( SP_1 \):
\[ SP_2 = (MP \times 0.80) \times 0.90 = MP \times 0.80 \times 0.90 = MP \times 0.72 \]

### Step 5: Set Up the Equation
We know that the final selling price \( SP_2 \) is ₹468:
\[ MP \times 0.72 = 468 \]

### Step 6: Solve for the Marked Price
Now, we can solve for \( MP \):
\[ MP = \frac{468}{0.72} \]
Calculating this gives:
\[ MP = 650 \]

### Conclusion
The marked price of the item is ₹650.

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