An article wassold for ₹98,496 after providing three successive discounts of 10%, 5% and 4% respectively on the marked price. What was the marked price?

Options

A. ₹1,10,700
B. ₹1,20,000
C. ₹1,20,200
D. ₹1,20,500

Answer

To find the marked price of the article after three successive discounts of 10%, 5%, and 4%, we can follow these steps:

### Step 1: Understand the Discounts
The article is sold for ₹98,496 after applying three successive discounts. We need to determine the marked price (let's denote it as \( M \)) before these discounts were applied.

### Step 2: Calculate the Effective Selling Price
The selling price after the discounts can be expressed as:
\[ \text{Selling Price} = M \times (1 - d_1) \times (1 - d_2) \times (1 - d_3) \]
where \( d_1, d_2, d_3 \) are the discounts in decimal form.

For the discounts:
- \( d_1 = 10\% = 0.10 \)
- \( d_2 = 5\% = 0.05 \)
- \( d_3 = 4\% = 0.04 \)

### Step 3: Substitute the Values
Substituting the values into the equation, we have:
\[ 98,496 = M \times (1 - 0.10) \times (1 - 0.05) \times (1 - 0.04) \]
This simplifies to:
\[ 98,496 = M \times 0.90 \times 0.95 \times 0.96 \]

### Step 4: Calculate the Product of Discounts
Now, calculate the product of the fractions:
\[ 0.90 \times 0.95 = 0.855 \]
\[ 0.855 \times 0.96 = 0.8196 \]

### Step 5: Set Up the Equation
Now, we can set up the equation:
\[ 98,496 = M \times 0.8196 \]

### Step 6: Solve for Marked Price
To find \( M \), we rearrange the equation:
\[ M = \frac{98,496}{0.8196} \]

### Step 7: Calculate the Marked Price
Now, perform the division:
\[ M \approx 120,000 \]

Thus, the marked price of the article is approximately ₹120,000.