A person sold two watches for Rs 5500 each. In the sale of the first watch, he made a profit of 20% and in the sale of the second watch, he incurred a 20% loss. What is his gain or loss percentage in total?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 4% loss
Profit and loss per cent are worked out on the cost price, so the two cost prices are found first. The two selling prices are equal, but the costs are not, so the 20% profit and the 20% loss do not cancel.
The two cost prices:
First watch, 20% profit: cost \(\displaystyle =5500\times\frac{100}{120}=\frac{13750}{3}\approx4583.33\)
Second watch, 20% loss: cost \(\displaystyle =5500\times\frac{100}{80}=6875\)
The totals:
Total cost \(\displaystyle =\frac{13750}{3}+6875=\frac{34375}{3}\approx11458.33\)
Total selling price \(=11000\)
The loss (on the total cost):
Loss \(\displaystyle =\frac{34375}{3}-11000=\frac{1375}{3}\approx458.33\)
Loss per cent \(\displaystyle =\frac{1375/3}{34375/3}\times100=\frac{1375}{34375}\times100=4\%\)
Shortcut: When two articles are sold at the same selling price, one at \(x\%\) profit and the other at \(x\%\) loss, there is always a loss of \(\displaystyle\frac{x^2}{100}\%\).
Here \(x=20\), so the loss is \(\displaystyle\frac{20^2}{100}=4\%\)