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A man bought an article for ₹800. He sold it at a profit of 15%. With that money, he bought another article and sold it at a loss of 10%. Find his overall gain/loss %.

Mathematics

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Step-by-step solution

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Here's how to solve the problem:

  1. Calculate the selling price of the first article.

    The man bought the first article for ₹800 and sold it at a profit of 15%.

    Selling Price (SP1)=Cost Price (CP1)×(1+Profit %100)\text{Selling Price (SP1)} = \text{Cost Price (CP1)} \times \left(1 + \frac{\text{Profit \%}}{100}\right) SP1=₹800×(1+15100)\text{SP1} = ₹800 \times \left(1 + \frac{15}{100}\right) SP1=₹800×(1+0.15)\text{SP1} = ₹800 \times (1 + 0.15) SP1=₹800×1.15=₹920\text{SP1} = ₹800 \times 1.15 = ₹920
  2. Calculate the selling price of the second article.

    With the money from the first sale (₹920), he bought another article. So, the cost price of the second article (CP2) is ₹920. He sold it at a loss of 10%.

    Selling Price (SP2)=Cost Price (CP2)×(1−Loss %100)\text{Selling Price (SP2)} = \text{Cost Price (CP2)} \times \left(1 - \frac{\text{Loss \%}}{100}\right) SP2=₹920×(1−10100)\text{SP2} = ₹920 \times \left(1 - \frac{10}{100}\right) SP2=₹920×(1−0.10)\text{SP2} = ₹920 \times (1 - 0.10) SP2=₹920×0.90=₹828\text{SP2} = ₹920 \times 0.90 = ₹828
  3. Calculate the overall gain or loss.

    The initial cost price was ₹800, and the final selling price was ₹828.

    Overall Gain/Loss=Final Selling Price−Initial Cost Price\text{Overall Gain/Loss} = \text{Final Selling Price} - \text{Initial Cost Price} Overall Gain/Loss=₹828−₹800=₹28\text{Overall Gain/Loss} = ₹828 - ₹800 = ₹28

    Since the result is positive, it's an overall gain.

  4. Calculate the overall gain percentage.

    Overall Gain %=Overall GainInitial Cost Price×100\text{Overall Gain \%} = \frac{\text{Overall Gain}}{\text{Initial Cost Price}} \times 100 Overall Gain %=₹28₹800×100\text{Overall Gain \%} = \frac{₹28}{₹800} \times 100 Overall Gain %=288=3.5%\text{Overall Gain \%} = \frac{28}{8} = 3.5\%

    The calculated overall gain is 3.5%. Comparing this to the given options:
    (A) 2% gain
    (B) 2% loss
    (C) 3% gain
    (D) 3% loss

    Since 3.5% gain is not an exact option, we choose the closest one. 3.5% gain is closer to 3% gain than to 2% gain.

    The final answer is C\boxed{\text{C}}

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