On a certain item, the initial profit is 120% of the cost price. If the cost price increases by 10% but the selling price remains the same, what will be the new profit percentage on the item?

Introduction / Context:
This question involves profit percentage with a change in cost price but a fixed selling price. Initially, the profit on an item is 120% of its cost. Later the cost increases by 10%, but the selling price is not changed. We need to compute how this affects the profit percentage. This tests understanding of how profit percentages are sensitive to changes in cost price when selling price remains constant.

Given Data / Assumptions:

• Initial profit = 120% of cost price.
• Let initial cost price be C.
• Initial profit = 1.2C, so selling price = C + 1.2C.
• Cost price increases by 10%, becoming 1.1C.
• Selling price stays the same as before.
• We must find the new profit percentage based on the new cost price.

Concept / Approach:
First compute the original selling price in terms of C:

• Original profit = 1.2C.
• Original selling price SP = C + 1.2C = 2.2C.

When cost price increases by 10%:

• New cost price = 1.1C.
• Selling price remains 2.2C.
• New profit = SP - new CP = 2.2C - 1.1C = 1.1C.
• New profit percentage = (1.1C / 1.1C) * 100.

Step-by-Step Solution:
Let initial cost price be C. Initial profit is 120% of C, so profit = 1.2C. Therefore, original selling price SP = C + 1.2C = 2.2C. Cost price increases by 10%, so new cost price CP2 = 1.1C. Selling price remains SP = 2.2C. New profit = SP - CP2 = 2.2C - 1.1C. New profit = 1.1C. New profit percentage = (1.1C / 1.1C) * 100 = 100%. So the new profit percentage is 100%.

Verification / Alternative check:
Choose a convenient cost price, for example C = 100 rupees initially.

• Initial profit = 120% of 100 = 120 rupees.
• Initial selling price = 100 + 120 = 220 rupees.
• New cost price after 10% increase = 110 rupees.
• Selling price remains 220 rupees.
• New profit = 220 - 110 = 110 rupees.
• New profit percent = (110 / 110) * 100 = 100%.

This simple numeric check confirms the algebraic solution.

Why Other Options Are Wrong:
Values like 50%, 60%, 90% or 75% do not arise from the given relations. Since the selling price is still much larger than the increased cost price, the profit percentage remains high. Specifically, the new profit is exactly equal to the new cost price, which implies a 100% profit, not any of the smaller percentages listed as distractors.

Common Pitfalls:
Many learners mistakenly treat the 120% as overall selling price rather than profit, or they add and subtract percentages without reference to the correct base. Another error is to compute the new profit percent still on the original cost price instead of the increased cost price. Always clearly define cost, selling price, and profit before and after the change, and be careful about which cost price you use when computing percentages.

Final Answer:
The new profit percentage on the item is 100%.