After allowing three successive discounts of `10% , 20% and 5%` on the market price of an article, it is sold for Rs. 2,394 . The cost price of the article is Rs. 2,500 . If it is sold at the marked price, then the profit will be
(a)Rs.1,000
(b)Rs. 950
(c)Rs. 960
(d)Rs. 1,050

Options

A. Rs. 1,000
B. Rs. 950
C. Rs. 960
D. Rs. 1,050

Answer

To solve the problem step by step, we will follow the process of calculating the marked price (MP) from the selling price (SP) after applying the successive discounts, and then determine the profit when sold at the marked price.

### Step 1: Understand the Discounts
We have three successive discounts:
- First discount: 10%
- Second discount: 20%
- Third discount: 5%

### Step 2: Calculate the Effective Discount
To find the effective discount after applying all three discounts, we can use the formula:
\[ \text{Effective Discount} = 1 - (1 - d_1)(1 - d_2)(1 - d_3) \]
Where \(d_1, d_2, d_3\) are the decimal forms of the discounts:
- \(d_1 = 0.10\)
- \(d_2 = 0.20\)
- \(d_3 = 0.05\)

Calculating the effective discount:
\[ \text{Effective Discount} = 1 - (0.90)(0.80)(0.95) \]
Calculating step by step:
1. \(0.90 \times 0.80 = 0.72\)
2. \(0.72 \times 0.95 = 0.684\)
3. Therefore, \(\text{Effective Discount} = 1 - 0.684 = 0.316\)

This means the effective discount is 31.6%.

### Step 3: Calculate the Selling Price (SP) from Marked Price (MP)
We know that the selling price after discounts is Rs. 2,394. We can express this as:
\[ SP = MP \times (1 - \text{Effective Discount}) \]
Substituting the values:
\[ 2394 = MP \times (1 - 0.316) \]
\[ 2394 = MP \times 0.684 \]

### Step 4: Solve for Marked Price (MP)
To find MP, we rearrange the equation:
\[ MP = \frac{2394}{0.684} \]
Calculating this gives:
\[ MP \approx 3500 \]

### Step 5: Calculate Profit
Now we can calculate the profit when sold at the marked price. The profit is given by:
\[ \text{Profit} = MP - CP \]
Where:
- CP (Cost Price) = Rs. 2,500

Substituting the values:
\[ \text{Profit} = 3500 - 2500 = 1000 \]

### Final Answer
The profit when sold at the marked price is Rs. 1,000.