Two phones are each sold for ₹1,200, one at a 20% profit and the other at a 20% loss. What is the overall profit or loss?
An overall loss of 4%, or ₹100. Costs are 1,200/1.2 = ₹1,000 and 1,200/0.8 = ₹1,500. Total cost ₹2,500, total sale ₹2,400. When selling prices are equal and the gain and loss percentages are equal, there is always a loss of x^2/100 %.
Explain it simply
It feels like a 20% gain and a 20% loss should cancel out. They do not, because the percentages are taken on different cost prices. The phone sold at a loss had to cost more to end up at the same ₹1,200, so the loss is on a bigger base and the rupees lost are more than the rupees gained.
Example
Question: Two items each sold at ₹1,200, one at 20% profit, the other at 20% loss. Net result?
- CP of the first = 1,200 / 1.2 = ₹1,000 (profit ₹200).
- CP of the second = 1,200 / 0.8 = ₹1,500 (loss ₹300).
- Total CP = ₹2,500, total SP = ₹2,400.
- Net loss = ₹100. Loss % = 100 / 2,500 x 100 = 4%.
Shortcut: loss % = x^2 / 100 = 20 x 20 / 100 = 4%.
const cp = 1200 / 1.2 + 1200 / 0.8;
console.log(Math.round(cp)); // Output: 2500
console.log(Math.round(((cp - 2400) / cp) * 100)); // Output: 4The shortcut works only when the selling prices are equal. If the cost prices are equal instead, a 20% gain and a 20% loss do cancel out exactly.
What to say in the interview
"The percentages are on different cost prices, so they don't cancel. The costs are 1,000 and 1,500, total 2,500, and sales total 2,400, a 4% loss. The shortcut is x squared over 100, valid when both selling prices are the same."
Common mistakes
- Saying no profit, no loss.
- Using the x^2/100 shortcut when cost prices, not selling prices, are equal.