Percentage, Profit & Loss • Topic 3 of 4

Profit, Loss & Cost Price

Profit = SP - CP, Loss = CP - SP, and crucially profit% and loss% are taken on the COST price. To get SP from a profit%, multiply CP by (1 + p/100). To recover CP from SP and a profit%, divide SP by (1 + p/100). When equal numbers of articles are bought and sold at different rates, set up per-unit cost and selling values.

✅ Solved examples

1. CP = 80, SP = 100. Profit %?
Profit = 20, profit% = 20/80 x 100 = 25%.
2. Buy at 5 each, want 40% profit. SP each?
SP = 5 x 1.40 = 7.
3. An article is sold for 1020 at a 15% loss. Find CP.
CP = 1020 / 0.85 = 1200.
4. By selling at 270 a man gains 8%. Find CP.
CP = 270 / 1.08 = 250.

✏️ Practice — try these, take hints as needed

1. Buy 60, sell 78. Profit %?
Profit = 18.
18/60.
x 100.
30%
2. CP 240, want 25% profit. SP?
x 1.25.
240 x 1.25.
—
300
3. Buy 150, sell 135. Loss %?
Loss = 15.
15/150.
x 100.
10%
4. Sold for 552 at 8% loss. CP?
CP = SP/0.92.
552/0.92.
—
600
5. Gain 20% by selling at 600. CP?
CP = 600/1.2.
—
—
500

📝 Topic test — 8 questions

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