In a certain store, the profit is 320% of the cost price of an item. If the cost price increases by 25% but the selling price remains unchanged, approximately what percentage of the selling price is now the profit?

Introduction / Context:
This question tests understanding of profit as a percentage of cost versus profit as a percentage of selling price. Initially, a very high profit is made relative to cost price. When the cost price increases but the selling price is held constant, the profit reduces, and the problem asks for this reduced profit expressed as a percentage of the selling price. This is a useful concept in commercial mathematics and retail pricing.

Given Data / Assumptions:

• Initial profit = 320% of cost price.
• Therefore, initially, profit = 3.2 times cost price.
• So initial selling price = cost price + profit.
• Cost price increases by 25%.
• Selling price remains constant at its original value.
• We must express the new profit as a percentage of the (unchanged) selling price.

Concept / Approach:
Let the original cost price be C. A profit of 320% of C means profit = 3.2 * C. Hence, initial selling price SP = C + 3.2C = 4.2C. When cost price increases by 25%, new cost price becomes 1.25C, while SP stays at 4.2C. The new profit is SP - new cost = 4.2C - 1.25C. Finally, the required percentage is (new profit / SP) * 100. Because C cancels out, we can work symbolically without needing actual numeric cost.

Step-by-Step Solution:
Step 1: Let original cost price = C. Step 2: Given profit = 320% of C, so profit = 3.2C. Step 3: Initial selling price SP = C + 3.2C = 4.2C. Step 4: New cost price after 25% increase = C * 1.25 = 1.25C. Step 5: Selling price is unchanged at SP = 4.2C. Step 6: New profit = SP - new cost = 4.2C - 1.25C = 2.95C. Step 7: Required profit percentage on SP = (2.95C / 4.2C) * 100. Step 8: The factor C cancels, so percentage = (2.95 / 4.2) * 100 ≈ 70.24%. Step 9: Approximating, this is about 70% of the selling price.

Verification / Alternative check:
Take a convenient value, for example C = Rs. 100. Then original profit = 320% of 100 = Rs. 320. Initial SP = 100 + 320 = Rs. 420. New CP after 25% rise = 125. New profit = 420 - 125 = Rs. 295. Profit as percentage of SP = (295 / 420) * 100 ≈ 70.24%, confirming our symbolic calculation and justifying the rounded answer of 70% as the closest option.

Why Other Options Are Wrong:
An 80% or 90% profit on the selling price would require the profit to be 0.8 or 0.9 times 420, which does not match 295. The value 60% is too low compared to the actual fraction of about 70.24%. Therefore, only 70% is a reasonable approximation based on the calculations.

Common Pitfalls:
Students sometimes confuse profit as a percentage of cost price with profit as a percentage of selling price, or misinterpret 320% profit as selling price being 320% of cost. Another frequent error is to increase the cost and selling prices together instead of holding the selling price constant as stated. Using a variable for cost and following the algebra carefully avoids these mistakes.

Final Answer:
After the cost increase, the profit is approximately 70% of the selling price.