Profit Loss Advanced
Key Concepts & Formulas
| # | Concept | Quick Explanation |
|---|---|---|
| 1 | Marked Price (MP) → Discount → Selling Price (SP) | SP = MP × (1 – d/100); always apply discount on MP |
| 2 | Total CP when articles bought in lots | Weighted average CP = (C₁Q₁ + C₂Q₂)/(Q₁+Q₂) |
| 3 | False weight & % gain | Gain % = (True weight – False weight)/False weight × 100 |
| 4 | Two articles sold at same SP, one at x% gain & other at x% loss | Net loss = x²/100 % (independent of SP) |
| 5 | Equivalent single discount | For successive d₁ & d₂, single discount = d₁+d₂–d₁d₂/100 |
| 6 | CP : SP : Profit given in ratio | If CP:SP = a:b, Profit % = (b–a)/a × 100 |
| 7 | Installment purchase interest | Total CP = Down-payment + PV of all installments (use simple interest formula) |
10 Practice MCQs
1. A trader marks his goods 60% above CP and gives a discount of 25%. Find the actual profit %.
A) 17% B) 20% C) 25% D) 30%Answer: B) 20%
Solution: Let CP = 100 → MP = 160; SP = 160×0.75 = 120 → Profit % = 20%.
Shortcut: Profit % = (100+60)(1–0.25) – 100 = 20%.
Concept tag: MP-Discount-Profit chain
2. Two bikes sold at Rs 36,000 each; first gains 20%, second loses 20%. Net result?
A) No loss no gain B) Loss Rs 3,000 C) Loss Rs 2,000 D) Gain Rs 1,500Answer: B) Loss Rs 3,000
Solution: CP₁ = 36000/1.2 = 30,000; CP₂ = 36000/0.8 = 45,000; Total CP = 75,000, SP = 72,000 → Loss 3,000.
Shortcut: Net loss = x²/100 % = 4% of average CP.
Concept tag: Same SP opposite gains
3. 950 gm instead of 1 kg sold at CP. Gain %?
A) 4.75% B) 5% C) 5.26% D) 6%Answer: C) 5.26%
Solution: Gain % = (1000–950)/950 × 100 ≈ 5.26%.
Concept tag: False weight
4. After 15% discount a man buys an article for Rs 1,530. What is the marked price?
A) 1,700 B) 1,800 C) 1,850 D) 1,900Answer: B) 1,800
Solution: MP × 0.85 = 1530 → MP = 1530/0.85 = 1800.
Concept tag: Discount base
5. A shopkeeper uses 880 gm for 1 kg and sells at 10% above CP. Real gain %?
A) 22% B) 23% C) 25% D) 27%Answer: C) 25%
Solution: CP for 880 gm = CP₀; SP for 880 gm = 1.1 CP₀; but customer pays for 1 kg.
Real SP = 1.1 CP₀ per 880 gm → per kg SP = 1.1 CP₀ ×1000/880 = 1.25 CP₀ → 25%.
Shortcut: Combine false weight & markup: (1000/880)×1.1 – 1 = 0.25.
Concept tag: False weight + markup
6. Cost price of 20 articles equals selling price of x articles. If profit is 25%, then x equals
A) 14 B) 16 C) 18 D) 25Answer: B) 16
Solution: 20 CP = x SP → SP/CP = 20/x; 1.25 = 20/x → x = 16.
Concept tag: CP-SP-article equivalence
7. A single discount equivalent to successive 20% and 10% is
A) 28% B) 29% C) 30% D) 32%Answer: A) 28%
Solution: 20+10–20×10/100 = 28%.
Concept tag: Successive discounts
8. A man sells two pens for Rs 48 each; on one he gains 20% and on the other loses 20%. Find the cost price of the pen sold at loss.
A) 60 B) 50 C) 55 D) 64Answer: A) 60
Solution: CP = 48/0.8 = 60.
Concept tag: Same SP opposite gains
9. Profit calculated on SP is 25%. What is the profit % on CP?
A) 20% B) 25% C) 33.33% D) 50%Answer: C) 33.33%
Solution: Profit = 0.25 SP → CP = 0.75 SP → Profit % on CP = 0.25/0.75 = 33⅓%.
Concept tag: Profit on SP vs CP
10. A dealer allows 10% discount on marked price and gets 20% profit. If MP = Rs 500, what is the CP?
A) 360 B) 375 C) 400 D) 425Answer: B) 375
Solution: SP = 500×0.9 = 450; CP = 450/1.2 = 375.
Concept tag: MP-Discount-Profit triangle
5 Previous Year Questions
[RRB NTPC 2021] A fruit-seller uses 900 g instead of 1 kg and sells at cost price. His gain % is
A) 10% B) 11.11% C) 12% D) 9.09%Answer: B) 11.11%
Solution: (1000–900)/900 × 100 = 11.11%.
[RRB Group-D 2019] Two TVs sold at Rs 24,000 each; one at 20% profit, other at 20% loss. Net result?
A) Loss Rs 2,000 B) Loss Rs 1,000 C) Gain Rs 1,000 D) No loss no gainAnswer: A) Loss Rs 2,000
Shortcut: x²/100 = 4% of average CP (50,000) → 2,000 loss.
[RRB JE 2018] After 25% discount, still 20% profit. What % is MP above CP?
A) 45% B) 50% C) 55% D) 60%Answer: D) 60%
Solution: CP = 100 → SP = 120; MP × 0.75 = 120 → MP = 160 → 60% above CP.
[RRB NTPC 2016] Single discount equivalent to 10%, 12% and 5% successive discounts is
A) 24.76% B) 25.24% C) 26% D) 27%Answer: A) 24.76%
Solution: 1–0.9×0.88×0.95 = 0.2476 → 24.76%.
[RRB ALP 2015] A man buys 11 pens for Rs 100 and sells 10 pens for Rs 110. Profit %?
A) 19% B) 20% C) 21% D) 22%Answer: C) 21%
Solution: CP per pen = 100/11; SP per pen = 110/10 = 11; Profit % = (11–100/11)/(100/11) × 100 = 21%.
Speed Tricks & Shortcuts
| Situation | Shortcut | Example |
|---|---|---|
| Same SP, opposite x% gain/loss | Net loss = x²/100 % | x=20 → 4% loss |
| Markup x%, discount y%, need profit z% | Required markup = (100+z)/(1–y/100) – 100 | y=25,z=20 → 60% |
| False weight gain | Multiply gains: (claimed/true)×(1+markup) – 1 | 900 g, 10% markup → (1000/900)×1.1–1 ≈ 22.22% |
| Two discounts d₁ & d₂ | Single = d₁+d₂–d₁d₂/100 | 20%,10% → 28% |
| CP:SP given in ratio a:b | Profit % = (b–a)/a × 100 | 4:5 → 25% |
Common Mistakes to Avoid
| Mistake | Why Students Make It | Correct Approach |
|---|---|---|
| Taking discount on CP instead of MP | Haste in reading | Always MP is base for discount |
| Using x% loss on SP as –x% profit | Sign confusion | Loss % is always computed on CP |
| Forgetting to convert false weight to per kg | Incomplete unitary method | Always normalize to 1 kg or 1 unit |
| Adding successive discounts directly | Treating like simple interest | Use 1–(1–d₁)(1–d₂) formula |
Quick Revision Flashcards
| Front | Back |
|---|---|
| Formula for single equivalent discount d₁ & d₂ | d₁+d₂–d₁d₂/100 |
| Net result when two articles sold at same SP with ±x% | Loss x²/100 % |
| Gain % when 800 g sold for 1 kg at CP | 25% |
| Relation CP:SP = 5:6 → Profit % | 20% |
| Profit on SP is 20% → Profit on CP | 25% |
| MP 50% above CP, discount 20% → Profit % | 20% |
| Two successive 10% discounts equal to single | 19% |
| If CP of 10 = SP of 8 → Profit % | 25% |
| Markup needed to get 10% profit after 10% discount | 22.22% |
| Quick ratio: CP:SP:Profit = 4:5:1 → Profit % | 25% |
BETA
