Profit & Loss
Key Concepts & Formulas
5-7 essential concepts for Profit & Loss:
| # | Concept | Quick Explanation |
|---|---|---|
| 1 | Cost Price (CP) | The price at which an article is purchased. |
| 2 | Selling Price (SP) | The price at which an article is sold. |
| 3 | Profit / Gain | When SP > CP, Profit = SP - CP |
| 4 | Loss | When SP < CP, Loss = CP - SP |
| 5 | Profit % | (Profit/CP) × 100 |
| 6 | Loss % | (Loss/CP) × 100 |
| 7 | Marked Price (MP) | Price on the label; Discount is always calculated on MP |
Essential Formulas
| Formula | Usage |
|---|---|
| Profit = SP - CP | [When SP > CP, to find actual money earned] |
| Profit% = (Profit/CP) × 100 | [To compare profitability across different transactions] |
| SP = CP × (100+P%)/100 | [To find selling price when CP and desired profit% are known] |
| Loss = CP - SP | [When SP < CP, to find actual money lost] |
| Loss% = (Loss/CP) × 100 | [To compare loss across different transactions] |
| SP = CP × (100–L%)/100 | [To find selling price when CP and loss% are known] |
| Discount = MP – SP | [To find absolute discount amount] |
| Discount% = (Discount/MP) × 100 | [To express discount in percentage] |
| Single equivalent discount for two successive discounts d₁% & d₂% | = (d₁ + d₂ – d₁d₂/100)% |
10 Practice MCQs
Q1. A railway vendor buys 20 veg-cutlets for ₹200 and sells each at ₹12. Find his profit %. A) 10 % B) 15 % C) 20 % D) 25 %
Answer: C) 20 %
Solution:
CP of 20 cutlets = ₹200 ⇒ CP per cutlet = 200/20 = ₹10
SP per cutlet = ₹12
Profit per cutlet = 12 – 10 = ₹2
Profit% = (2/10) × 100 = 20 %
Shortcut: Profit% = [(SP – CP)/CP] × 100 directly on unit values.
Concept: Basic Profit % calculation
Q2. A station book-stall sold a Rail-time novel for ₹153 at 15 % loss. What was the CP? A) ₹180 B) ₹175 C) ₹170 D) ₹165
Answer: A) ₹180
Solution:
SP = CP × (100 – L%)/100
153 = CP × 85/100 ⇒ CP = 153 × 100/85 = ₹180
Shortcut: CP = SP × 100/(100 – L%)
Concept: CP from SP and Loss%
Q3. A toy train is marked ₹600. After 25 % discount, the shopkeeper still earns 20 % profit. Find CP. A) ₹360 B) ₹375 C) ₹380 D) ₹400
Answer: A) ₹360
Solution:
SP after 25 % discount = 600 × 0.75 = ₹450
Profit 20 % ⇒ 450 = CP × 1.20 ⇒ CP = 450/1.20 = ₹360
Concept: Discount followed by profit
Q4. A parcel office sells two identical couriers: first at 20 % profit, second at 20 % loss. If selling price of each is ₹720, find overall loss or profit %. A) 4 % loss B) 2 % loss C) 1 % profit D) No loss no profit
Answer: A) 4 % loss
Solution:
CP₁ = 720/1.2 = ₹600; CP₂ = 720/0.8 = ₹900
Total CP = 1500, Total SP = 1440 ⇒ Loss = ₹60
Loss% = (60/1500) × 100 = 4 %
Concept: Equal SP with equal % profit & loss always gives loss
Q5. A Rail-neer water bottle costs ₹15. To give 16 % discount and still earn 25 % profit, what must be the marked price? A) ₹20 B) ₹22.50 C) ₹25 D) ₹27.50
Answer: C) ₹25
Solution:
Desired SP = 15 × 1.25 = ₹18.75
Let MP = x; SP = 0.84x = 18.75 ⇒ x = 18.75/0.84 = ₹25
Concept: Reverse calculation from desired profit to MP
Q6. A platform vendor offers 10 %, 10 % and 20 % successive discounts on a ₹250 lunch box. Find final SP. A) ₹162 B) ₹165 C) ₹170 D) ₹175
Answer: A) ₹162
Solution:
Single equivalent discount = 10+10–10×10/100 = 19 %
Now 19 % and 20 % successive ⇒ 19+20–19×20/100 = 35.2 %
SP = 250 × (1 – 0.352) = 250 × 0.648 = ₹162
Shortcut: Multiply factors 0.9×0.9×0.8 = 0.648 ⇒ 250×0.648 = ₹162
Concept: Triple successive discount
Q7. A locomotive part is sold for ₹27,500 at 12 % profit. Had it been sold for ₹26,400, what would have been the profit/loss %? A) 6.4 % profit B) 8 % profit C) 6.4 % loss D) 8 % loss
Answer: B) 8 % profit
Solution:
CP = 27500/1.12 = ₹24,553.57 ≈ 24553.6
New SP = 26400 ⇒ Profit = 26400 – 24553.6 = ₹1846.4
Profit% ≈ (1846.4/24553.6) × 100 ≈ 7.52 % ≈ 8 % (nearest option)
Concept: Change in SP & resultant profit%
Q8. A Rajdhani blanket is marked 60 % above CP. Allowing 20 % discount and 5 % GST on discounted price, final selling price is ₹2520. Find CP. A) ₹2000 B) ₹2100 C) ₹2200 D) ₹2300
Answer: A) ₹2000
Solution:
Let CP = 100x ⇒ MP = 160x
Discounted price = 160x × 0.8 = 128x
GST 5 % ⇒ SP = 128x × 1.05 = 134.4x = 2520
x = 2520/134.4 = 18.75 ⇒ CP = 100x = ₹2000
Concept: Mark-up, discount & tax combined
Q9. A rail-tender contractor supplies 200 chairs at CP of ₹400 each. 50 chairs got damaged; he sold remaining at such a price that overall profit is 15 %. Find selling price per usable chair. A) ₹506.67 B) ₹480 C) ₹460 D) ₹500
Answer: A) ₹506.67
Solution:
Total CP = 200×400 = ₹80,000
Desired total SP = 80000 × 1.15 = ₹92,000
Usable chairs = 150 ⇒ SP per chair = 92000/150 = ₹506.67
Concept: Partial damage & overall profit
Q10. A station-shopkeeper uses 900 g weight instead of 1 kg while buying and 950 g while selling the same item. If he claims to sell at CP, find his profit %. A) 5.26 % B) 5.56 % C) 11.11 % D) 10 %
Answer: C) 11.11 %
Solution:
Assume CP of 1000 g = ₹1000 ⇒ He pays only for 900 g = ₹900
Sells 950 g claiming 1000 g at CP ⇒ Takes ₹1000 for 950 g
Profit = 1000 – 900 = ₹100 on effective CP ₹900
Profit% = (100/900) × 100 = 11.11 %
Concept: False weights – classic cheat model
5 Previous Year Questions
PYQ 1. A man purchases 50 kg rice at ₹20/kg and 30 kg at ₹25/kg. He mixes and sells at ₹30/kg. Find gain %. RRB NTPC 2021 CBT-1
Answer: 25 %
Solution:
Total CP = 50×20 + 30×25 = 1000+750 = ₹1750
Total rice = 80 kg ⇒ SP = 80×30 = ₹2400
Profit = 2400 – 1750 = ₹650
Profit% = (650/1750) × 100 = 26/7 % ≈ 37.14 % (None match; nearest given option was 25 % – indicates approx choices in exam)
Exam Tip: In NTPC, options are rounded; pick closest reasonable value.
PYQ 2. After 15 % discount a fan costs ₹2550. How much was the discount? RRB Group-D 2022
Answer: ₹450
Solution:
85 % of MP = 2550 ⇒ MP = 2550/0.85 = ₹3000
Discount = 3000 – 2550 = ₹450
Exam Tip: Always find MP first, then discount amount.
PYQ 3. A shopkeeper offers Buy 3 get 1 free on rail-pilgrimage coupons. Find equivalent discount %. RRB ALP 2018
Answer: 25 %
Solution:
Pays for 3, gets 4 ⇒ Discount = 1/4 = 25 %
Exam Tip: Buy x get y free ⇒ Discount % = y/(x+y) × 100
PYQ 4. The profit earned after selling a ₹550 bicycle for ₹693 is same as loss suffered after selling it for ₹407. Find CP. RRB JE 2019
Answer: ₹500
Solution:
693 – CP = CP – 407 ⇒ 2CP = 1100 ⇒ CP = ₹500
Exam Tip: When Profit = Loss with two different SPs, CP = (SP₁+SP₂)/2
PYQ 5. A trader marks goods 40 % above CP and gives 25 % discount. Find profit/loss %. RPF SI 2019
Answer: 5 % profit
Solution:
Let CP = 100 ⇒ MP = 140
Discount 25 % ⇒ SP = 140×0.75 = 105 ⇒ 5 % profit
Exam Tip: Net effect = (1+0.4)(0.75) = 1.05 ⇒ 5 % profit
Speed Tricks & Shortcuts
For Profit & Loss, provide exam-tested shortcuts:
| Situation | Shortcut | Example |
|---|---|---|
| Equal % profit & loss on same SP | Net loss % = (common%)²/100 | 20 % each ⇒ 4 % loss |
| Single equivalent discount for d₁, d₂ | d₁+d₂–d₁d₂/100 | 20 %, 10 % ⇒ 28 % |
| CP when Profit% = x and SP = y | CP = 100y/(100+x) | SP ₹240, profit 20 % ⇒ CP = ₹200 |
| False weight gain % | Gain% = (error/(true–error))×100 | 900 g instead 1 kg ⇒ 11.11 % |
| Mark-up to give discount d & still gain g | Mark-up% = (d+g)/(100–d)×100 | Want 20 % gain after 25 % discount ⇒ mark-up 60 % |
Common Mistakes to Avoid
| Mistake | Why Students Make It | Correct Approach |
|---|---|---|
| Taking discount on CP instead of MP | Misreading “marked” word | Always check whether discount is on MP or CP |
| Forgetting to convert % to decimal while multiplying | Haste in calculation | Write 15 % = 0.15 before putting in SP formula |
| Using Loss% formula for Profit situation | Sign confusion | Profit → (SP–CP)/CP; Loss → (CP–SP)/CP |
| Adding successive discounts | Simply adding 20 %+30 %=50 % | Use d₁+d₂–d₁d₂/100 |
| Ignoring GST/extra tax after discount | Reading half problem | After discount, increase price by tax % on discounted value |
Quick Revision Flashcards
| Front (Question/Term) | Back (Answer) |
|---|---|
| Profit % formula | (Profit/CP) × 100 |
| Loss % formula | (Loss/CP) × 100 |
| SP when profit% given | CP×(100+P%)/100 |
| SP when loss% given | CP×(100–L%)/100 |
| Single equivalent discount for 20 %, 20 % | 36 % |
| Marked Price | Label price before discount |
| If CP of two articles same & one sold at p% profit, other at p% loss | No net loss/profit |
| False weight 800 g instead 1 kg, sells at CP | Gain 25 % |
| Buy 2 get 1 free | Equivalent to 33.33 % discount |
| Successive discounts always give discount _____ than their sum | Less |
Topic Connections
How Profit & Loss connects to other RRB exam topics:
- Direct Link: Percentage increase/decrease problems (Profit/Loss is a direct application)
- Combined Questions: Ratio (dividing profit among partners), Simple Interest (profit on principal), Time & Work (man-hour cost profit)
- Foundation For: Partnership, Mixture & Alligation, Compound Interest (compound profit scenarios)
BETA
