Two articles are sold at the same selling price. The first is sold at a profit of 20% and the second at a loss of 20%. Find the overall profit or loss percentage.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Loss of 4%
Take a convenient common selling price and find each cost price; compare the total cost with the total selling price.
Let each SP be Rs 9600
CP of the first \(=9600\div1.2=8000\); CP of the second \(=9600\div0.8=12000\)
Total CP \(=20000\), total SP \(=19200\)
Loss \(=800\), which is \(4\%\) of the CP
There is an overall loss of 4%.
Why the other options are incorrect
Option (2) Loss of 8% — Incorrect. This doubles the loss; the overall loss is \(\displaystyle\frac{20^{2}}{100}\%\).
Option (3) No profit, no loss — Incorrect. The profit and the loss are on different cost prices, so they do not cancel; the article sold at a loss cost more.
Option (4) Profit of 4% — Incorrect. There is a loss, not a profit, because the article sold at a loss had the larger cost price.