Question:

A store sells two pieces of electronic items, one at 20% profit and another at 10% loss, respectively, thereby making an overall profit of 6%. What is the ratio of the cost prices of the two items?

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When calculating the ratio of cost prices in profit and loss problems, set up an equation based on the overall profit percentage.
Updated On: Sep 30, 2025
  • 8 : 9
  • 1 : 1
  • 8 : 7
  • 4 : 3
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The Correct Option is A

Solution and Explanation

Step 1: Let the cost prices of the two items be \( x \) and \( y \).
The profit on the first item is \( 0.20x \), and the loss on the second item is \( 0.10y \).
Step 2: Overall profit equation.
The overall profit is 6%, so: \[ \frac{0.20x - 0.10y}{x + y} = 0.06 \] \[ 0.20x - 0.10y = 0.06(x + y) \] \[ 0.20x - 0.10y = 0.06x + 0.06y \] \[ 0.20x - 0.06x = 0.10y + 0.06y \] \[ 0.14x = 0.16y \] \[ \frac{x}{y} = \frac{0.16}{0.14} = \frac{8}{9} \]
Final Answer: \[ \boxed{8 : 9} \]
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