A dealer sold two types of goods for 10,000 each. On one of them, he lost 20% and on the other he gained 20%. His gain or loss percent in the entire transaction was ?
Show Hint
When two items are sold at the same price, and one has a P% profit and the other a P% loss, there is *always* a net loss. The loss percentage is simply $\left(\frac{P}{10}\right)^2\%$. Remember this shortcut for efficiency in competitive exams.
Take the cost price of each item as a base value of 100 to make the comparison easy.
2% loss: This is too small compared with what the base-100 comparison below gives, so it is not the answer.
2% gain: Selling one item at a loss and the other at an equal gain, with the same selling price for both, can never produce an overall gain, so this is ruled out.
4% gain: For the same reason, a net gain is impossible in this kind of transaction, so this option is incorrect.
4% loss: Assume each item has a cost price of 100 units. Sold at a 20% loss, the selling price is 80; sold at a 20% gain, the selling price is 120. To make both selling prices equal to the real value of Rs. 10,000, scale each base by the required factor: item one needs a factor of \( \frac{10000}{80} = 125 \), giving CP \( = 100\times125 = 12{,}500 \); item two needs a factor of \( \frac{10000}{120} = 83.33 \), giving CP \( \approx 8{,}333.33 \). Total CP \( \approx 20{,}833.33 \) against total SP of Rs. 20,000, a loss of about Rs. 833.33, which is \( \frac{833.33}{20{,}833.33}\times 100 = 4\% \).