Multiple choice

If two items sold at the same price Rs. 1864 each, one at a loss of 19% and the other at a profit of 19%, then find the overall loss and loss percentage.

  1. Rs. 150 and 5%

  2. Rs. 139.62 and 3.61%

  3. Rs. 245 and 4.45%

  4. Rs. 164 and 3.86%

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For two items sold at the same price with equal percentage profit and loss, the overall result is always a loss. The loss percentage is (x^2)/100 = (19^2)/100 = 3.61%. With SP = 1864 each, CP1 = 1864/0.81 = 2301.23 and CP2 = 1864/1.19 = 1566.39. Total CP = 3867.62, Total SP = 3728. Loss = 3867.62 - 3728 = 139.62.

AI explanation

When two items are sold at the same price but at equal percentages of profit and loss, there is always an overall loss calculated by the formula total loss equals X squared divided by 100, where X is the percentage. Substituting 19 into the formula gives 19 times 19 divided by 100, resulting in an overall loss of 3.61 percent. The total selling price of the two items is 1864 plus 1864, equaling 3728 rupees, and the total cost price is 3728 divided by 0.9639, which equals approximately 3867.62 rupees. The overall loss in rupees is 3867.62 minus 3728, which gives a loss of Rs. 139.62.

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