An article is sold for Rs. 799.50 after allowing two successive discounts of 18% and 22% on its marked price. The cost price of the article is Rs. 1,000. If it is sold at the marked price. then the gain is:
(a)250
(b)240
(c)300
(d)220

Options

A. Rs. 250
B. Rs. 240
C. Rs. 300
D. Rs. 220

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Understand the Discounts
The article is sold for Rs. 799.50 after applying two successive discounts of 18% and 22%. We need to find the marked price (MP) first.

### Step 2: Calculate the Selling Price after Discounts
Let the marked price be \( MP \).

The selling price after the first discount of 18%:
\[ SP_1 = MP \times \left(1 - \frac{18}{100}\right) = MP \times 0.82 \]

After applying the second discount of 22% on the already discounted price:
\[ SP = SP_1 \times \left(1 - \frac{22}{100}\right) = (MP \times 0.82) \times 0.78 \]
Thus,
\[ SP = MP \times 0.82 \times 0.78 \]

### Step 3: Set the Selling Price Equal to Rs. 799.50
We know that the selling price \( SP \) is Rs. 799.50. Therefore, we can write:
\[ 799.50 = MP \times 0.82 \times 0.78 \]

### Step 4: Calculate the Combined Discount Factor
Calculating \( 0.82 \times 0.78 \):
\[ 0.82 \times 0.78 = 0.6396 \]

### Step 5: Solve for Marked Price (MP)
Now, substituting back into the equation:
\[ 799.50 = MP \times 0.6396 \]
To find \( MP \):
\[ MP = \frac{799.50}{0.6396} \approx 1249.23 \]

### Step 6: Round the Marked Price
For simplicity, we can round \( MP \) to Rs. 1250.

### Step 7: Calculate the Gain if Sold at Marked Price
The cost price (CP) of the article is Rs. 1,000. If sold at the marked price, the gain can be calculated as:
\[ \text{Gain} = MP - CP = 1250 - 1000 = 250 \]

### Conclusion
The gain when sold at the marked price is Rs. 250.

### Final Answer
(a) 250

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