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35% of goods were sold at a profit of 65%, while the remaining were sold at x% loss. If the overall loss is 12%, then what is the value of x? (correct to one decimal place)Options52.451.850.653.5

Question

35% of goods were sold at a profit of 65%, while the remaining were sold at x% loss. If the overall loss is 12%, then what is the value of x? (correct to one decimal place)Options52.451.850.653.5

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Solution

Let's solve this step by step:

  1. Let's assume the total cost of the goods is 100 units (this simplifies the calculation and doesn't affect the percentage result).

  2. 35% of the goods were sold at a profit of 65%. So, the profit from this part is 35 * 0.65 = 22.75 units.

  3. The remaining 65% of the goods were sold at a loss of x%. So, the loss from this part is 65 * x/100 = 0.65x units.

  4. The overall loss is 12%, which means a loss of 12 units.

  5. The total profit and loss should add up to the overall loss, so we can set up the following equation: 22.75 - 0.65x = -12.

  6. Solving this equation for x gives us: x = (22.75 + 12) / 0.65 = 53.5.

So, the value of x is 53.5%.

This problem has been solved

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