Prashanth sold an album for $735 and made a profit of 22.5%. Later the cost price of the album increased by $120, so he also increased his selling price by $120. What is his new profit percentage?

Introduction / Context:
This question is a profit and loss problem with a change in both cost price and selling price. First, we are told about an original sale with a known profit percentage. Then the cost increases by a fixed amount and the selling price is also increased by the same amount. We must compute the new profit percentage based on the new cost and new selling price.

Given Data / Assumptions:
- Original selling price (SP1) is 735 dollars.
- Original profit percentage is 22.5 percent.
- The cost price then increases by 120 dollars.
- The new selling price (SP2) is old selling price plus 120 dollars, that is SP2 = 735 + 120.
- We must find the new profit percentage based on the new cost price and new selling price.

Concept / Approach:
The basic relationship is profit = selling price - cost price, and profit percentage = (profit / cost price) * 100. First we find the original cost price from the given original selling price and profit percentage. Then we add 120 to this cost to get the new cost price. Similarly, we add 120 to the old selling price to get the new selling price. Finally, we compute the new profit percentage using the new figures.

Step-by-Step Solution:
Let original cost price be CP1. Given original profit is 22.5%, so SP1 = CP1 * (1 + 22.5 / 100). So 735 = CP1 * 1.225. Therefore, CP1 = 735 / 1.225 = 600. Now cost price increases by 120 dollars, so new cost price CP2 = 600 + 120 = 720. New selling price SP2 = 735 + 120 = 855. New profit = SP2 - CP2 = 855 - 720 = 135. New profit percentage = (135 / 720) * 100. Compute 135 / 720 = 0.1875, so profit percentage = 18.75%.

Verification / Alternative check:
We can confirm the original profit: with CP1 = 600 and SP1 = 735, profit1 = 135. Profit percentage1 = (135 / 600) * 100 = 22.5%, which matches the given condition, so CP1 is correct. For the new situation, CP2 = 720 and SP2 = 855, profit2 = 135 again, but now relative to a larger cost price. New profit percentage = 135 / 720 * 100 = 18.75%. This confirms the calculation.

Why Other Options Are Wrong:
19.32%, 21.41%, and 22%: These values do not match the exact ratio of 135 to 720 and arise from incorrect arithmetic or misunderstanding that profit amount remains the same but base cost changes.
20%: This is a nice round number but does not match the precise computation of 135 / 720.

Common Pitfalls:
One mistake is assuming the profit percentage remains the same because both cost price and selling price are increased by the same absolute amount. This is not true because profit percentage depends on the ratio of profit to the new cost price, which has changed. Another error is to misinterpret 22.5 percent as a fraction that is difficult to handle, but converting the percentage into a decimal (1.225) makes the calculation straightforward.

Final Answer:
Prashanth's new profit percentage after the cost and selling price both increase by $120 is 18.75 percent.