A trader allows two successive discounts of 30% and 40% on selling an article. If he sells that article for Rs 840, then what is the marked price (in Rs) of the article?

Options

A. a)2000
B. b)1900
C. c)1800
D. d)1700

Answer

To find the marked price of the article after applying two successive discounts of 30% and 40%, we can follow these steps:

### Step-by-Step Solution:

1. **Assume the Marked Price**:
Let's assume the marked price (MP) of the article is Rs 100. This makes calculations easier, as we can easily convert the percentages into actual values.

**Hint**: Start with a simple assumption to simplify calculations.

2. **Calculate the Selling Price after the First Discount**:
The first discount is 30% of the marked price.
- Discount amount = 30% of 100 = 30.
- Selling Price after first discount = Marked Price - Discount = 100 - 30 = Rs 70.

**Hint**: Calculate the discount by multiplying the marked price by the discount percentage.

3. **Calculate the Selling Price after the Second Discount**:
The second discount is 40% of the new selling price (Rs 70).
- Discount amount = 40% of 70 = 28.
- Selling Price after second discount = Selling Price after first discount - Discount = 70 - 28 = Rs 42.

**Hint**: Apply the second discount to the new selling price obtained after the first discount.

4. **Set up the Equation with the Actual Selling Price**:
We know that the final selling price after both discounts is Rs 840.
- Therefore, we can set up the equation:
\[ 42 \text{ (the calculated selling price)} = \text{Selling Price} \text{ (actual)} = 840. \]

**Hint**: Use the calculated selling price to relate it to the actual selling price.

5. **Find the Value of One Unit**:
To find the value of one unit in terms of the actual selling price, we divide:
\[ \text{Value of one unit} = \frac{840}{42} = 20. \]

**Hint**: Divide the actual selling price by the calculated selling price to find the unit value.

6. **Calculate the Marked Price**:
Since we assumed the marked price was Rs 100, and we found that one unit corresponds to Rs 20, we can find the actual marked price:
\[ \text{Actual Marked Price} = 100 \times 20 = Rs 2000. \]

**Hint**: Scale the assumed marked price by the value of one unit to find the actual marked price.

### Final Answer:
The marked price of the article is Rs 2000.