By selling two items at the same price, a person gains 20% on one item and loses 20% on the other. Then over all  

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CSIR-UGC (NET) Mathematical Science: Held on (2024 June)
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  1. he neither loses nor gains. 
  2. he loses 5%. 
  3. he loses 4%
  4. he gains 4%

Answer (Detailed Solution Below)

Option 3 : he loses 4%
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Detailed Solution

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Concept:

 Net loss = \(\left( \frac{\text{Common gain/loss percentage}}{10} \right)^2 \%\)

Explanation:

If a person gains \(x\% \) on one item and loses \(x\% \) on another item, the net result will always be a loss. 


Net loss = \(\left( \frac{\text{Common gain/loss percentage}}{10} \right)^2 \%\)

Here, the common percentage is 20%, so the net loss is

\(\text{Net loss} = \left( \frac{20}{10} \right)^2 = 2^2 = 4\%\)

Therefore, the person incurs a net loss of 4%.

Thus, the correct option is Option 3).

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