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A sells 2 TV sets, one at a loss of 15% and another at a profit of 15%. Find the loss/gain percentage in the overall transaction?

I assume the price of two TVs to be 100 and that of one to be 50. According to me there should be no profit or loss. However, the answer is 2.25% profit. Can somebody please explain to me how to solve this question?

Curious
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  • Are the prices of the TV sets the same? Why do you assume that the other one has price 50 (as opposed to 100) ? – Matti P. Dec 16 '20 at 13:03
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    If to not assume anything, we can set the prices to be $p_1$ and $p_2$. How do we calculate the loss/gain percentage? Well, the ratio is equal to actual price divided by the intended price (times 100%). So $$ \frac{\text{actual price}}{\text{intended price}} = \frac{(1-0.15)p_1 + (1+0.15) p_2}{p_1+p_2} $$ Without further information, this is as far as we can go. – Matti P. Dec 16 '20 at 13:04

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