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A man sells two articles at the same selling price- one at 15% profit and other at 15% loss. What is the overall profit or loss percentage?

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10% profit

5% profit

12.5% loss

2.25% loss

answer is C.

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Detailed Solution

Given that a man sold two articles at the same selling price- one at 15% profit and other at 15% loss.
For the first article,

SP = Rs . S

Given,

profit % = 15

\Rightarrow \frac{SP - CP}{CP} \times 100 = Profit %

\Rightarrow \frac{S - CP₁}{CP₁} \times 100 = 15

\Rightarrow \frac{S - CP₁}{CP₁} \times 100 = 15

\Rightarrow S - CP₁ = 0.15 \times CP₁

\Rightarrow S = CP₁ + 0.15 CP₁

\Rightarrow 1.15 \times CP₁ = S

\Rightarrow CP₁ = \frac{S}{1.15}

\Rightarrow CP₁ = \frac{S \times 100}{1.15 \times 100}

\Rightarrow CP₁ = \frac{100 S}{115}

\Rightarrow CP₁ = \frac{20 S}{23}

For the second article,

SP = Rs . S

From the given,

loss = 15

\Rightarrow \frac{CP - SP}{CP} \times 100 = 15

\Rightarrow \frac{CP₂ - S}{CP₂} \times 100 = 15

\Rightarrow CP₂ - S = 0.15 \times CP₂

\Rightarrow CP₂ - 0.15 CP₂ = S

\Rightarrow 0.85 CP₂ = S

\Rightarrow CP₂ = \frac{S}{0.85}

\Rightarrow CP₂ = \frac{S \times 100}{0.85 \times 100}

\Rightarrow CP₂ = \frac{100 S}{85}

\Rightarrow CP₂ = \frac{20 S}{17}

So,
Total SP of the two articles

= Rs . S + Rs . S

\Rightarrow

Total SP of the two articles

= Rs . 2 S

Total CP of the two articles

= Rs . \frac{20 S}{23} + Rs . \frac{20 S}{17}

\Rightarrow Total CP of the two articles = Rs . \frac{340 S + 460 S}{391}

\Rightarrow Total CP of the two articles = Rs . \frac{800 \times S}{391}

\Rightarrow Total CP of the two articles = Rs . 2.046 \times S

As total CP > SP, there is a loss.
So, Loss %

= \frac{CP - SP}{CP} \times 100

\Rightarrow Loss % = \frac{2.046 S - 2 S}{2.046 S} \times 100

\Rightarrow Loss % = \frac{0.046 S}{2.046 S} \times 100

\Rightarrow Loss % = 2.25

%
Thus, the loss is 2.25%.
Therefore the correct option is 3.

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