Profit, Loss & Discount • Topic 2 of 6

Profit & Loss %

Profit % and loss % are ALWAYS taken on the cost price, never the selling price — this single fact resolves most CAT errors here. As multipliers: SP = CP × (1 + p/100) for a profit, SP = CP × (1 − l/100) for a loss. To go backwards, divide: CP = SP ÷ (1 ± rate/100). A favourite CAT trap is "x articles bought for the price of y sold": profit % = (y − x)/x × 100 when you buy x at the price of y. Another classic is selling two items at the same SP, one at +x% and one at −x%: there is ALWAYS a net loss of (x/10)² %, regardless of the common selling price, because the gain base and the loss base differ. When goods are sold "at cost price but with a false weight", the gain is real and computed on the short weight, covered in the False Weights topic.

✅ Solved examples

1. CP ₹250, SP ₹300. Find the profit %.
Profit = 50 on CP 250 ⇒ (50/250) × 100 = 20%.
2. An item sold for ₹720 at a 20% profit. Find the cost price.
CP = 720 ÷ 1.20 = ₹600.
3. A shopkeeper buys 12 oranges for the price of 10 and sells at marked price. Find the profit %.
Buy 12 at the price of 10 ⇒ profit on 10 = 2 ⇒ (2/10) × 100 = 20%.
4. Two watches are each sold for ₹990, one at 10% profit and one at 10% loss. Find the overall result.
Same SP, ±10% ⇒ net loss = (10/10)² = 1%. CP1 = 990/1.1 = 900, CP2 = 990/0.9 = 1100, total CP 2000, total SP 1980 ⇒ ₹20 loss = 1%.

✏️ Practice — try these, take hints as needed

1. CP ₹400, SP ₹360. Loss %?
Loss on CP.
40/400 × 100.
Simplify.
10%
2. SP ₹575 at a 15% profit. Cost price?
CP = SP ÷ 1.15.
575/1.15.
Divide, don’t subtract 15%.
₹500
3. A man buys 15 pens for the price of 12 and sells at the printed price. Profit %?
Gain = 3 pens on a base of 12.
3/12 × 100.
Profit on the buying base.
25%
4. Two items each sold at ₹600, one at +20% and one at −20%. Net %?
Same SP, equal ± rate.
Loss = (rate/10)².
(20/10)².
4% loss
5. By selling at ₹126 a trader loses 10%. SP needed for a 20% profit?
CP = 126 ÷ 0.9 = 140.
New SP = CP × 1.2.
140 × 1.2.
₹168

📝 Topic test — 8 questions

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