The marked price of an article is increased by 25%, and the selling price is increased by 16.66%, so that the amount of profit doubles. If the original marked price was Rs. 400 and this was 33.33% higher than the corresponding cost price, what is the new increased selling price?

Introduction / Context:
This profit and loss question involves both a marked price (labelled price) and a selling price, with changes applied to each. The key condition is that the profit amount doubles after increasing both prices by given percentages. Combined with a relationship between marked price and cost price, the problem requires determining the new selling price. It tests multi-step percentage reasoning and equation setup.

Given Data / Assumptions:

• Original marked price = Rs. 400.
• The original marked price is 33.33% (one-third) higher than cost price.
• Therefore, cost price CP is such that 400 = CP * (1 + 1 / 3).
• Marked price is increased by 25%.
• Selling price is increased by 16.66% (approximately one-sixth).
• As a result, the profit amount doubles.
• We must find the new increased selling price.

Concept / Approach:
First, we find the original cost price from the relation between marked price and cost price. Then we let the original selling price be S. Original profit = S - CP. After changes, marked price does not directly affect cost but indicates that the new selling price is 1.1666 times S (approximately 7 / 6 times S). The new profit is then new selling price minus CP, and this is given to be double the original profit. This yields an equation in S, which we can solve and then use to find the new selling price.

Step-by-Step Solution:
Step 1: Original marked price = Rs. 400 is 33.33% higher than CP, so 400 = CP * (4 / 3).Step 2: Therefore CP = 400 * 3 / 4 = Rs. 300.Step 3: Let original selling price be S. Then original profit = S - 300.Step 4: Selling price is increased by 16.66%, which is approximately 1 / 6, so new selling price = S * (1 + 1 / 6) = 7S / 6.Step 5: New profit = (7S / 6) - 300.Step 6: Given that the new profit is double the original profit, so (7S / 6) - 300 = 2(S - 300).Step 7: Simplify: 7S / 6 - 300 = 2S - 600. Multiply through by 6: 7S - 1800 = 12S - 3600.Step 8: Rearrange: 1800 = 5S, so S = 360.Step 9: New selling price = 7S / 6 = 7 * 360 / 6 = 7 * 60 = Rs. 420.

Verification / Alternative check:
Original profit = S - CP = 360 - 300 = Rs. 60.New profit with selling price Rs. 420: 420 - 300 = Rs. 120.The new profit is indeed double the original profit (120 compared to 60), confirming the correctness of S and the new selling price.

Why Other Options Are Wrong:
A new selling price of Rs. 360 is simply the original selling price and does not change profit. Rs. 240 would represent a loss relative to the cost price of Rs. 300. Rs. 480 or Rs. 600 would produce profit amounts much higher than double the original profit. Only Rs. 420 gives exactly double the original profit while matching the given percentage change.

Common Pitfalls:
Some learners try to double the profit percentage instead of doubling the absolute profit amount, which changes the problem. Others mistakenly apply the percentage increases to cost price rather than to marked price and selling price. It is also easy to round 16.66% incorrectly and introduce noticeable errors. Carefully distinguishing each base and working with exact fractions such as 1 / 3 and 1 / 6 avoids these issues.

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