The marked price of an article is increased by 25 percent and its selling price is increased by 16.66 percent. As a result, the amount of profit doubles. If the original marked price was Rs. 400 and this marked price was 33.33 percent above the corresponding cost price, what is the new increased selling price?

Introduction / Context:
This question combines markup, selling price changes, and profit calculations. It tells us that after increasing both the marked price and selling price by given percentages, the monetary profit doubles. Using the original relationship between cost price and marked price, we can determine the original selling price, then calculate the new selling price after the increase.

Given Data / Assumptions:

• Original marked price MP0 = Rs. 400.
• Original marked price is 33.33 percent above cost price.
• Marked price is increased by 25 percent to a new marked price MP1.
• Selling price is increased by 16.66 percent to a new selling price SP1.
• The amount of profit doubles when going from original selling price SP0 to new selling price SP1.
• We must find SP1, the increased selling price.

Concept / Approach:
First determine the cost price using the given markup over cost. Then represent the original selling price as SP0 and write the profit as SP0 minus cost price. Next, the new selling price SP1 is 16.66 percent higher than SP0, so SP1 equals SP0 multiplied by a factor of approximately 7 / 6. The profit after the increase is SP1 minus cost price. The condition that profit doubles allows us to form an equation in SP0, which we can solve to get SP0 and then SP1.

Step-by-Step Solution:
Let the cost price be C. Original marked price MP0 = 400, which is 33.33 percent above cost. Thus 400 = C * (1 + 1 / 3) = (4 / 3) * C. So C = 400 * 3 / 4 = 300 rupees. Let SP0 be the original selling price. Original profit = SP0 - 300. New selling price SP1 is 16.66 percent greater than SP0. 16.66 percent is approximately 1 / 6, so SP1 = SP0 * (1 + 1 / 6) = (7 / 6) * SP0. New profit = SP1 - 300 = (7 / 6) * SP0 - 300. Given that new profit is double original profit: (7 / 6) * SP0 - 300 = 2 * (SP0 - 300). Multiply both sides to clear fraction: 7 * SP0 - 1800 = 12 * SP0 - 3600. Rearrange: 12 * SP0 - 7 * SP0 = 3600 - 1800. 5 * SP0 = 1800, so SP0 = 360 rupees. Therefore SP1 = (7 / 6) * 360 = 420 rupees.

Verification / Alternative check:
Original profit = SP0 - cost = 360 - 300 = 60 rupees. New profit = SP1 - cost = 420 - 300 = 120 rupees. The profit amount has doubled from Rs. 60 to Rs. 120 as required, so the new selling price of Rs. 420 is correct.

Why Other Options Are Wrong:
Rs. 380, Rs. 440, Rs. 460: These selling prices do not produce exactly double the original profit when checked against the cost price of Rs. 300. Only Rs. 420 satisfies both the profit doubling condition and the given selling price increase of 16.66 percent.

Common Pitfalls:
Some candidates mistakenly apply the 25 percent increase in marked price directly to selling price or assume that original selling price equals original marked price. Others misinterpret 16.66 percent and use approximate values in a way that changes the result. Working with simple rational equivalents like 1 / 6 for 16.66 percent helps to keep calculations clear and exact.

Final Answer:
The increased selling price of the article is Rs. 420.