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Profit, Loss, Discount — Formulas

Quantitative Aptitude · Profit, Loss & Discount

Useful for: SSC CGL

Overview

Profit or loss is always on cost price; discount is always on marked price — keeping the two bases separate solves almost every item.

Key points

Profit % = (SP − CP)/CP × 100; Loss % = (CP − SP)/CP × 100.
SP = CP × (100 + profit%)/100; SP = MP × (100 − discount%)/100.
Dishonest dealer using a false weight: gain % = (true − false)/false × 100.
Selling two items at the same SP, one at x% profit and one at x% loss, gives an overall loss of x²/100 %.
Mark-up m% and discount d% → profit % = m − d − md/100.

Explanation

If CP of x items = SP of y items: profit % = (x − y)/y × 100.
"Buy 3 get 1 free" is a discount of 1/4 = 25% on the marked price.
Use CP = 100 as a convenient base for comparison questions.
Discount is never calculated on cost price.

Step by step

Mark CP, MP and SP.
Apply the formula on the correct base.
Check whether the answer is profit or loss.

Examples

CP ₹400, SP ₹460 → profit 60/400 × 100 = 15%.
MP ₹800, discount 15% → SP ₹680; if CP is ₹600, profit = 80/600 × 100 = 13.33%.
A shopkeeper uses a 900 g weight for 1 kg: gain = 100/900 × 100 = 11.11%.

Traps and advanced points

Trap: Calculating profit % on SP instead of CP.
Trap: Calculating discount on CP instead of MP.
Trap: Assuming equal profit and loss on the same SP cancel out.

Quick revision

Profit on CP, discount on MP.
Same SP, ±x% → loss x²/100 %.
m − d − md/100 for mark-up with discount.

Practice MCQs

A shopkeeper sells an article at Rs 720 gaining 20%. The cost price is:
1. Rs 600
2. Rs 576
3. Rs 640
4. Rs 620
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Answer: (a) Rs 600. SP = CP(1+20/100) = 1.2×CP = 720 → CP = 720/1.2 = 600.
By selling 33 articles, a man loses an amount equal to the selling price of 3 articles. His loss percent is:
1. 9%
2. 10%
3. 7.5%
4. 8.33%
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Answer: (d) 8.33%. SP of 33 = 33s.
A dishonest dealer sells goods at cost price but uses a weight of 900 g for 1 kg. His profit percent is:
1. 11.11%
2. 10%
3. 9%
4. 12.5%
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Answer: (a) 11.11%. Formula: (Error/(True-Error))×100 = (100/900)×100 = 11.11%.
A man buys two articles for Rs 1000 each. He sells one at 20% profit and other at 20% loss. His overall result is:
1. 4% profit
2. 2% loss
3. No profit no loss
4. 4% loss
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Answer: (c) No profit no loss. Yahan CP alag-alag hain (equal CP), same % profit-loss → net zero.
After allowing a discount of 12.5%, a trader still gains 20%. The marked price is above cost price by:
1. 37.14%
2. 35%
3. 40%
4. 32%
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Answer: (a) 37.14%. CP=100 → SP=120.
A sells to B at 25% profit, B sells to C at 20% profit. If C pays Rs 900, A's cost price was:
1. Rs 600
2. Rs 640
3. Rs 675
4. Rs 720
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Answer: (a) Rs 600. A→B: CP×1.25.
The cost price of 20 articles equals the selling price of 16 articles. The profit percent is:
1. 25%
2. 20%
3. 16%
4. 30%
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Answer: (a) 25%. 20 CP = 16 SP → SP/CP = 20/16 = 5/4.
An article marked at Rs 500 is sold after two successive discounts of 10% and 20%. The selling price is:
1. Rs 350
2. Rs 340
3. Rs 370
4. Rs 360
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Answer: (d) Rs 360. 500 × 0.9 × 0.8 = 500 × 0.72 = 360.
If selling price is doubled, the profit triples. The original profit percent is:
1. 75%
2. 100%
3. 50%
4. 200%
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Answer: (b) 100%. Let CP=x, SP=y, profit=y-x.
A trader gains 15% after allowing 15% discount on marked price. If MP is Rs 460, cost price is (approx):
1. Rs 340
2. Rs 360
3. Rs 320
4. Rs 300
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Answer: (a) Rs 340. SP = MP×0.85 = 460×0.85 = 391.

Notes and questions are written by Kundali IQ for practice. They are not official papers; always check the latest official notification for the syllabus and pattern.