Two dealers offer an item at the same marked price, Rs.2,000. Due to the festive season, the first dealer allows successive discounts of 25% and 15%, and the other dealer allows successive discounts of 10% and 30%. At what price is the item available in the better offer?

Options

A. Rs. 1,275
B. Rs. 1,250
C. Rs. 1,260
D. Rs. 1,255

Answer

To solve the problem, we need to calculate the final selling prices of the item from both dealers after applying their respective discounts.

### Step 1: Calculate the total discount for the first dealer.
The first dealer offers successive discounts of 25% and 15%. We can use the formula for total discount when two successive discounts are given:

\[ \text{Total Discount} = X + Y - \frac{XY}{100} \]

Here, \(X = 25\%\) and \(Y = 15\%\).

\[ \text{Total Discount} = 25 + 15 - \frac{25 \times 15}{100} \]

Calculating the product:

\[ 25 \times 15 = 375 \]

Now substituting back into the formula:

\[ \text{Total Discount} = 25 + 15 - \frac{375}{100} = 40 - 3.75 = 36.25\% \]

### Step 2: Calculate the selling price for the first dealer.
The marked price is Rs. 2000. We will now calculate the selling price after applying the total discount of 36.25%.

\[ \text{Selling Price} = \text{Marked Price} - \left(\frac{\text{Total Discount}}{100} \times \text{Marked Price}\right) \]

Substituting the values:

\[ \text{Selling Price} = 2000 - \left(\frac{36.25}{100} \times 2000\right) \]

Calculating the discount amount:

\[ \frac{36.25}{100} \times 2000 = 725 \]

Now, substituting this back:

\[ \text{Selling Price} = 2000 - 725 = 1275 \]

### Step 3: Calculate the total discount for the second dealer.
The second dealer offers successive discounts of 10% and 30%. We will use the same formula:

\[ \text{Total Discount} = 10 + 30 - \frac{10 \times 30}{100} \]

Calculating the product:

\[ 10 \times 30 = 300 \]

Now substituting back into the formula:

\[ \text{Total Discount} = 10 + 30 - \frac{300}{100} = 40 - 3 = 37\% \]

### Step 4: Calculate the selling price for the second dealer.
Using the marked price of Rs. 2000 and the total discount of 37%:

\[ \text{Selling Price} = 2000 - \left(\frac{37}{100} \times 2000\right) \]

Calculating the discount amount:

\[ \frac{37}{100} \times 2000 = 740 \]

Now substituting this back:

\[ \text{Selling Price} = 2000 - 740 = 1260 \]

### Step 5: Compare the selling prices.
- Selling price from the first dealer: Rs. 1275
- Selling price from the second dealer: Rs. 1260

The better offer is from the second dealer, as the item is available for Rs. 1260.

### Final Answer:
The item is available at a better offer price of **Rs. 1260**.

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