Question:
What percent of selling price would be 34% of cost price if gross profit is 26% of the selling price?
What percent of selling price would be 34% of cost price if gross profit is 26% of the selling price?
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Express cost price in terms of selling price when dealing with percentage-based profit calculations to simplify the equation.
Updated On: Mar 7, 2025
- 17.16%
- 74%
- 25.16%
- 88.40%
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The Correct Option is C
Solution and Explanation
Let the selling price be \( S \) and the cost price be \( C \).
Given that the gross profit is 26% of the selling price: \[ S - C = 0.26S \] Rearrange to express \( C \) in terms of \( S \): \[ C = S - 0.26S = 0.74S \] Now, we are given that 34% of cost price is: \[ 0.34C = x% \text{ of } S \] Substituting \( C = 0.74S \): \[ 0.34 \times 0.74S = x% \times S \] \[ 0.2516S = x% \times S \] \[ x = 25.16% \] Thus, the required percentage is 25.16%.
Given that the gross profit is 26% of the selling price: \[ S - C = 0.26S \] Rearrange to express \( C \) in terms of \( S \): \[ C = S - 0.26S = 0.74S \] Now, we are given that 34% of cost price is: \[ 0.34C = x% \text{ of } S \] Substituting \( C = 0.74S \): \[ 0.34 \times 0.74S = x% \times S \] \[ 0.2516S = x% \times S \] \[ x = 25.16% \] Thus, the required percentage is 25.16%.
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