If the selling price of an item is tripled and its cost price is doubled, the profit becomes 65%. What is the present profit percentage on the item?

Introduction / Context:
This question describes a hypothetical change in both selling price and cost price and tells us the resulting profit percentage. From that altered situation, we need to deduce what the original profit percentage was. It checks your ability to form algebraic equations with unknown cost and selling prices and to interpret percentages correctly.

Given Data / Assumptions:

• Original cost price is C and original selling price is S.
• New cost price is doubled, that is 2C.
• New selling price is tripled, that is 3S.
• Under these new conditions, profit percentage becomes 65%.
• We have to find the original profit percentage based on original C and S.

Concept / Approach:
Profit percentage is defined as Profit / Cost * 100. For the new scenario, profit is 3S - 2C and cost is 2C. Given profit percentage is 65%, so (3S - 2C) / (2C) * 100 = 65. This gives an equation relating S and C. Solving for S in terms of C allows us to calculate original profit percentage, which is (S - C) / C * 100.

Step-by-Step Solution:
Let original cost price be C and original selling price be S.In the modified case, cost price = 2C and selling price = 3S.Profit in modified case = 3S - 2C.Given profit percentage in modified case = 65%, so (3S - 2C) / (2C) * 100 = 65.Thus (3S - 2C) / (2C) = 0.65.3S - 2C = 0.65 * 2C = 1.3C.3S = 2C + 1.3C = 3.3C, so S = 3.3C / 3 = 1.1C.Original profit = S - C = 1.1C - C = 0.1C.Original profit percentage = (0.1C / C) * 100 = 10%.

Verification / Alternative check:
To verify numerically, assume C = Rs 100. Then S = 1.1 * 100 = Rs 110. Original profit percentage is (110 - 100) / 100 * 100 = 10%. In the modified scenario, cost becomes 2 * 100 = Rs 200 and selling price becomes 3 * 110 = Rs 330. Profit = 330 - 200 = Rs 130. Profit percentage = 130 / 200 * 100 = 65%, which matches the given condition and confirms that the original profit percentage is 10%.

Why Other Options Are Wrong:
Profit percentages like 15%, 20% or 25% correspond to different relationships between S and C, leading to different values of 3S - 2C in the modified scenario. For these values, the profit percentage in the modified case would not be 65%. Only a 10% original profit is consistent with the equation derived from the given information.

Common Pitfalls:
Some students incorrectly treat the change as 3S - 2C equal to 65 directly or forget to divide by 2C when setting up the percentage equation. Another error is mixing up which quantity is doubled and which is tripled. Carefully aligning the profit formula with the modified values avoids these mistakes.

Final Answer:
The present profit percentage on the item is 10%.