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Profit, Loss & Discount

Quantitative Aptitude / DI · Arithmetic Applications

Useful for: Railway RRB, IBPS Banking, CTET, OTET, OSSTET, UGC NET, OSSC RHT — Regular High School Teacher, CSIR NET

and 20 more exams

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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

An article costs ₹3600. It is sold at 20% profit. Find the selling price.
1. 4500
2. 4320
3. 4680
4. 4140
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Answer: (b) 4320. SP = CP × (100+20)/100.
An article costs ₹4150. It is sold at 15% profit. Find the selling price.
1. 4980
2. 5187.5
3. 4772.5
4. 4565
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Answer: (c) 4772.5. SP = CP × (100+15)/100.
An article costs ₹4650. It is sold at 10% profit. Find the selling price.
1. 5115
2. 4882.5
3. 5580
4. 5347.5
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Answer: (a) 5115. SP = CP × (100+10)/100.
An article costs ₹5150. It is sold at 25% profit. Find the selling price.
1. 6437.5
2. 6952.5
3. 6180
4. 6695
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Answer: (a) 6437.5. SP = CP × (100+25)/100.
An article costs ₹800. It is sold at 12% profit. Find the selling price.
1. 936
2. 896
3. 976
4. 856
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Answer: (b) 896. SP = CP × (100+12)/100.
An article costs ₹2800. It is sold at 8% profit. Find the selling price.
1. 2884
2. 3164
3. 3304
4. 3024
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Answer: (d) 3024. SP = CP × (100+8)/100.
An article costs ₹3350. It is sold at 25% profit. Find the selling price.
1. 4522.5
2. 4020
3. 4187.5
4. 4355
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Answer: (c) 4187.5. SP = CP × (100+25)/100.
An article costs ₹3900. It is sold at 20% profit. Find the selling price.
1. 5070
2. 4680
3. 4875
4. 4485
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Answer: (b) 4680. SP = CP × (100+20)/100.
An article costs ₹4450. It is sold at 15% profit. Find the selling price.
1. 5562.5
2. 5340
3. 4895
4. 5117.5
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Answer: (d) 5117.5. SP = CP × (100+15)/100.
An article costs ₹4950. It is sold at 10% profit. Find the selling price.
1. 5692.5
2. 5445
3. 5197.5
4. 5940
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Answer: (b) 5445. SP = CP × (100+10)/100.
An article costs ₹650. It is sold at 25% profit. Find the selling price.
1. 812.5
2. 877.5
3. 780
4. 845
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Answer: (a) 812.5. SP = CP × (100+25)/100.
An article costs ₹850. It is sold at 15% profit. Find the selling price.
1. 1062.5
2. 935
3. 1020
4. 977.5
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Answer: (d) 977.5. SP = CP × (100+15)/100.
An article costs ₹600. It is sold at 20% profit. Find the selling price.
1. 750
2. 690
3. 720
4. 780
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Answer: (c) 720. SP = CP × (100+20)/100.
An article costs ₹450. It is sold at 10% profit. Find the selling price.
1. 472.5
2. 517.5
3. 540
4. 495
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Answer: (d) 495. SP = CP × (100+10)/100.
An article costs ₹500. It is sold at 12% profit. Find the selling price.
1. 535
2. 585
3. 610
4. 560
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Answer: (d) 560. SP = CP × (100+12)/100.