The profit earned by selling an article for Rs 900 is exactly double the loss incurred when the same article is sold for Rs 490. Based on this information, at what price should the article be sold in order to earn a profit of 25 percent on its cost price?

Introduction / Context:
This profit and loss question connects the selling price at which profit is made with another selling price at which a loss is incurred on the same article. The profit in one case is given as double the loss in the other case. From that relationship we first determine the cost price of the article. Once the cost price is known, we then compute the new selling price that will yield a 25 percent profit. This type of problem is very common in commerce and aptitude exams.

Given Data / Assumptions:
- When the article is sold for Rs 900, there is a profit.
- When the article is sold for Rs 490, there is a loss.
- The profit at Rs 900 is double the loss at Rs 490.
- The cost price is the same in all cases and does not change.
- We are required to find the selling price that gives 25 percent profit on the cost price.

Concept / Approach:
Let the cost price be C. Profit at a given selling price is selling price minus cost price. Loss at a given selling price is cost price minus selling price. The relation "profit is double the loss" forms an equation in C. After solving for C, we calculate the selling price that corresponds to a 25 percent profit by multiplying the cost price by 1.25. Due to the arithmetic, the resulting selling price is a fractional amount, which we present in both exact and approximate form.

Step-by-Step Solution:
Step 1: Let the cost price be C rupees. Step 2: Profit when selling at Rs 900 = 900 − C. Step 3: Loss when selling at Rs 490 = C − 490. Step 4: Given that profit is double the loss, so 900 − C = 2 * (C − 490). Step 5: Expand the right side: 900 − C = 2C − 980. Step 6: Bring variables on one side: 900 + 980 = 3C, so 1880 = 3C. Step 7: Therefore C = 1880 / 3 rupees. Step 8: For a profit of 25 percent, selling price S = C * 1.25 = (1880 / 3) * (5 / 4) = 2350 / 3 rupees. Step 9: 2350 / 3 ≈ 783.33 rupees (rounded to two decimal places).

Verification / Alternative check:
Check the original condition using the computed cost price. Profit at Rs 900 is 900 − 1880/3 = (2700 − 1880) / 3 = 820/3. Loss at Rs 490 is 1880/3 − 490 = (1880 − 1470) / 3 = 410/3. Clearly 820/3 = 2 * (410/3), so the profit is indeed double the loss, which confirms our cost price. Then a 25 percent gain on C is equal to C * 1.25, which we computed accurately as 2350/3 rupees.

Why Other Options Are Wrong:
Option Rs 750: This would correspond to a cost price of Rs 600, which does not satisfy the given double profit loss relation.
Option Rs 715: Does not match the exact fractional value 2350/3 and so does not represent a 25 percent profit on the correct cost price.
Option Rs 400: This is less than even the loss making selling price of Rs 490, so it cannot represent a 25 percent profit scenario.

Common Pitfalls:
Learners sometimes mistakenly assume the new selling price must be a nice integer matching one of the original prices, or they may incorrectly set up the equation for profit and loss. Another common error is to treat 25 percent profit directly on the selling price rather than on the cost price. Always express profit and loss in terms of cost price and use the relationships carefully.

Final Answer:
The article should be sold for approximately Rs 783.33 to earn a 25 percent profit.