Loss – When Selling Price Is Less Than Cost Price
A loss occurs when something is sold for less than it cost. Just as with profit, the loss is expressed as a percentage of the cost price so that different transactions can be compared fairly.
Key Terms
| Term | Meaning |
|---|---|
| Cost Price (CP) | What you paid to buy or make the item |
| Selling Price (SP) | What you sold the item for |
| Loss | CP minus SP (when CP is greater than SP) |
| Loss % | Loss expressed as a percentage of the cost price |
Formulas
Loss = Cost Price minus Selling Price. Loss % = (Loss / Cost Price) times 100.
Worked Examples
A laptop bought for 900 is sold for 675.
Loss = 900 - 675 = 225. Loss % = (225 / 900) times 100 = 25%.
A car bought for 12,000 is sold for 9,600.
Loss = 12000 - 9600 = 2400. Loss % = (2400 / 12000) times 100 = 20%.
Find the selling price if CP = 500 and loss = 15%.
Loss amount = 15% of 500 = 75. SP = 500 - 75 = 425. Or: SP = 500 times 0.85 = 425.
Find the cost price if SP = 357 and loss = 10%.
SP = CP times 0.90. CP = 357 / 0.90 = 396.67.
Loss vs Profit Comparison
| Profit | Loss | |
|---|---|---|
| When | SP greater than CP | SP less than CP |
| Amount | SP - CP | CP - SP |
| % Formula | (Profit/CP) x 100 | (Loss/CP) x 100 |
| Multiplier | 1 + rate/100 | 1 - rate/100 |
Key Takeaways
- Loss = CP minus SP. CP is always greater when there is a loss.
- Loss% is always calculated on the cost price.
- To find SP given CP and loss%: SP = CP times (1 - loss%/100).
- To find CP given SP and loss%: CP = SP / (1 - loss%/100).
Practice Questions
- A bicycle bought for 180 is sold for 135. Find the loss and loss %.
- A phone bought for 320 is sold for 256. Find the loss %.
- An item is sold at a loss of 20% for 64. Find the cost price.
- A trader buys 100 items at 5 each and sells 80 at 4.50 each. The remaining 20 are unsold. Find overall profit or loss.
- A house bought for 200,000 is sold for 185,000. What is the percentage loss?