For an article, the profit is 190% of the cost price. If the cost price increases by 10% but the selling price remains the same, then the new profit is what percentage (approximately) of the selling price?

Introduction / Context:
This question explores how profit relationships change when cost price changes but selling price remains constant. Initially, profit is very high, equal to 190% of the cost price. Then the cost price increases by 10%, but the selling price does not change. We are asked to express the new profit as a percentage of the selling price instead of the cost price. This is a multi-step percentage problem that tests careful reasoning and algebraic manipulation.

Given Data / Assumptions:

• Initial profit is 190% of the cost price.
• Let the original cost price be C.
• Thus, original profit P1 = 1.90 * C.
• Original selling price S = C + P1.
• Cost price then increases by 10% to a new cost price C2 = 1.10 * C.
• Selling price remains S.
• We need to find the new profit as a percentage of S.

Concept / Approach:
First, we express the original selling price in terms of C. Since profit is 190% of C, P1 = 1.90C and S = C + 1.90C = 2.90C. After increasing the cost price by 10%, the new cost price becomes 1.10C. The new profit is then S − C2. Once we express this new profit as a multiple of C, we can form the ratio (New profit / S) * 100 to get the required percentage of selling price. This requires careful handling of both old and new values in symbolic form.

Step-by-Step Solution:
Let original cost price be C.Given original profit P1 = 190% of C = 1.90C.Original selling price S = C + P1 = C + 1.90C = 2.90C.Now cost price increases by 10%, so new cost price C2 = 1.10C.Selling price remains S = 2.90C.New profit P2 = S − C2 = 2.90C − 1.10C = 1.80C.We must express P2 as a percentage of S.So required percentage = (P2 / S) * 100 = (1.80C / 2.90C) * 100.The C terms cancel, giving (1.80 / 2.90) * 100.Compute the fraction: 1.80 / 2.90 ≈ 0.6207.Therefore, percentage ≈ 0.6207 * 100 ≈ 62.07%.Approximately, the new profit is 62% of the selling price.

Verification / Alternative check:
Take a numerical example: let C = Rs. 100 for simplicity.Original profit = 190% of 100 = Rs. 190; original selling price S = 100 + 190 = Rs. 290.New cost price = 10% more than 100 = Rs. 110.New profit = S − new cost = 290 − 110 = Rs. 180.Express this as a percentage of selling price: (180 / 290) * 100 ≈ 62.07%.Rounded to the nearest integer, this is 62%, validating our algebraic solution.

Why Other Options Are Wrong:
54% and 73% deviate significantly from the precise ratio 180/290 and result from incorrect manipulation of percentages.163% confuses profit as a percentage of cost price with profit as a percentage of selling price.The approximation closest to the true value is 62%, which is the only correct choice.

Common Pitfalls:
A frequent misunderstanding is to treat the 190% profit as a percentage of selling price instead of cost price.Some learners add 10% directly to 190% to get 200% and attempt to use that for selling price calculations, which is incorrect.Others compute the new profit percentage with respect to the new cost price instead of the selling price as explicitly asked.

Final Answer:
After the 10% increase in cost price (with selling price unchanged), the new profit is approximately 62% of the selling price.