In a certain business, the profit is 220 percent of the cost price. If the cost price increases by 25 percent but the selling price remains unchanged, then approximately what percentage of the selling price does the new profit represent?

Introduction / Context:
This question relates profit to both cost price and selling price, and examines what happens when the cost price changes but the selling price does not. Initially the profit is very high relative to cost. After a cost increase, the absolute profit falls even though the selling price is unchanged. The problem asks us to express the new profit as a percentage of the selling price, which is a slightly different base than usual.

Given Data / Assumptions:

• Initial profit is 220 percent of cost price.
• Cost price then increases by 25 percent.
• Selling price remains the same as before.
• We must find what percentage of the selling price the new profit is, approximately.
• All prices are positive and we assume usual definitions of profit.

Concept / Approach:
Let the original cost price be C. The original profit is 220 percent of C, so profit equals 2.20 * C and selling price equals cost plus profit equals 3.20 * C. After the cost increase of 25 percent, the new cost price becomes 1.25 * C, while selling price remains 3.20 * C. The new profit is selling price minus new cost, and the question asks for this new profit as a percentage of the selling price. Therefore, we compute the ratio of the new profit to the selling price and then multiply by 100.

Step-by-Step Solution:
Let initial cost price be C rupees.Initial profit equals 220 percent of C, so P equals 2.20 * C.Initial selling price S equals C plus P which is C + 2.20 * C equals 3.20 * C.Now cost price increases by 25 percent, so new cost price C1 equals 1.25 * C.Selling price stays S equals 3.20 * C.New profit P1 equals S minus C1 equals 3.20 * C minus 1.25 * C which is 1.95 * C.New profit as a fraction of selling price equals P1 divided by S equals (1.95 * C) / (3.20 * C) which simplifies to 1.95 / 3.20.Compute this ratio: 1.95 / 3.20 equals approximately 0.609375.Convert to percentage by multiplying by 100 to get about 60.94 percent, which is approximately 61 percent.

Verification / Alternative check:
We can assume a convenient cost price, for example C equals 100 rupees, to verify. Then selling price S equals 3.20 * 100 equals 320 rupees. After the 25 percent increase, new cost becomes 125 rupees. New profit equals 320 minus 125 equals 195 rupees. Profit as a percentage of selling price equals 195 divided by 320 multiplied by 100 which is again about 60.94 percent. This numerical example confirms the earlier algebraic calculation.

Why Other Options Are Wrong:
Option 75 percent would require a profit of 0.75 times the selling price, which would mean the cost price is much lower than 25 percent above the original. Option 55 percent underestimates the actual ratio. Option 81 percent would represent a profit very close to the selling price, which contradicts the fact that the cost increased by 25 percent. The only option close to the computed value of about 60.94 percent is 61 percent.

Common Pitfalls:
Some learners mix up profit percentage on cost price with profit percentage on selling price and try to compare the two directly. Others forget that the selling price remains fixed and recalculate it using the new cost. Keeping track of which quantity changes and which remains constant is critical. It is usually easier to assume a simple numeric value for cost price, perform all calculations, and then translate the final ratio into a percentage of the selling price.

Final Answer:
After the cost increase, the profit is approximately 61 percent of the selling price.