Numerical answer
A trader sold two watches for ₹1,980 each. On one he gained 10% and on the other he lost 10%. What was his overall loss, in rupees?
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Answer: 40
Find each cost price from its selling price.
- Watch sold at 10% gain: CP = 1980 ÷ 1.1 = 1800.
- Watch sold at 10% loss: CP = 1980 ÷ 0.9 = 2200.
Total CP = 4000; total SP = 3960. Loss = ₹40.
Shortcut: When two items are sold at the same price, one at x% gain and one at x% loss, the result is always a loss of x²/100 % of the total cost: here 1% of 4000 = 40. It is a loss because the item sold at a loss cost more.
- Watch sold at 10% gain: CP = 1980 ÷ 1.1 = 1800.
- Watch sold at 10% loss: CP = 1980 ÷ 0.9 = 2200.
Total CP = 4000; total SP = 3960. Loss = ₹40.
Shortcut: When two items are sold at the same price, one at x% gain and one at x% loss, the result is always a loss of x²/100 % of the total cost: here 1% of 4000 = 40. It is a loss because the item sold at a loss cost more.
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