Profit & Loss

Key Concepts & Formulas

5-7 essential concepts for Profit & Loss:

Essential Formulas

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:

Common Mistakes to Avoid

Quick Revision Flashcards

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)